Derive the Sum of a Finite Geometric Series Formula to Solve Problems: CCSS.Math.Content.HSA-SSE.B.4 - Algebra
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Identify the following sequence as arithmetic, geometric, or neither.
Identify the following sequence as arithmetic, geometric, or neither.
To identify the sequence as either arithmetic or geometric, first recall the difference between the two. An arithmetic sequence means that there is a common difference between the terms. If a sequence is geometric, then there is a common ratio between the terms.
Looking at the given sequence,
subtract the first term from the second term to find the common difference.
From here, add the common difference to the second term. If the sum is the third term, then the sequence is arithmetic.
Adding the common difference to each term in the sequence results in the next term in the sequence which makes this particular sequence, arithmetic.
To identify the sequence as either arithmetic or geometric, first recall the difference between the two. An arithmetic sequence means that there is a common difference between the terms. If a sequence is geometric, then there is a common ratio between the terms.
Looking at the given sequence,
subtract the first term from the second term to find the common difference.
From here, add the common difference to the second term. If the sum is the third term, then the sequence is arithmetic.
Adding the common difference to each term in the sequence results in the next term in the sequence which makes this particular sequence, arithmetic.
Compare your answer with the correct one above
Identify the following sequence as arithmetic, geometric, or neither.
Identify the following sequence as arithmetic, geometric, or neither.
To identify the sequence as either arithmetic or geometric, first recall the difference between the two. An arithmetic sequence means there exists a common difference between the terms. If a sequence is geometric, then there exists a common ratio between the terms.
Looking at the given sequence,
subtract the first term from the second term to find the common difference.
From here, add the common difference to the second term. If the sum is the third term, then the sequence is arithmetic.
Adding the common difference to each term in the sequence results in the next term in the sequence which makes this particular sequence, arithmetic.
To identify the sequence as either arithmetic or geometric, first recall the difference between the two. An arithmetic sequence means there exists a common difference between the terms. If a sequence is geometric, then there exists a common ratio between the terms.
Looking at the given sequence,
subtract the first term from the second term to find the common difference.
From here, add the common difference to the second term. If the sum is the third term, then the sequence is arithmetic.
Adding the common difference to each term in the sequence results in the next term in the sequence which makes this particular sequence, arithmetic.
Compare your answer with the correct one above
Identify the following sequence as arithmetic, geometric, or neither.
Identify the following sequence as arithmetic, geometric, or neither.
To identify the sequence as either arithmetic or geometric, first recall the difference between the two. An arithmetic sequence means there exists a common difference between the terms. If a sequence is geometric, then there exists a common ratio between the terms.
Looking at the given sequence,
subtract the first term from the second term to find the common difference.
From here, add the common difference to the second term. If the sum is the third term, then the sequence is arithmetic.
Adding the common difference to each term in the sequence results in the next term in the sequence which makes this particular sequence, arithmetic.
To identify the sequence as either arithmetic or geometric, first recall the difference between the two. An arithmetic sequence means there exists a common difference between the terms. If a sequence is geometric, then there exists a common ratio between the terms.
Looking at the given sequence,
subtract the first term from the second term to find the common difference.
From here, add the common difference to the second term. If the sum is the third term, then the sequence is arithmetic.
Adding the common difference to each term in the sequence results in the next term in the sequence which makes this particular sequence, arithmetic.
Compare your answer with the correct one above
Identify the following sequence as arithmetic, geometric, or neither.
Identify the following sequence as arithmetic, geometric, or neither.
To identify the sequence as either arithmetic or geometric, first recall the difference between the two. An arithmetic sequence means there exists a common difference between the terms. If a sequence is geometric, then there exists a common ratio between the terms.
Looking at the given sequence,
subtract the first term from the second term to find the common difference.
From here, add the common difference to the second term.
If adding the common difference to each term in the sequence results in next term then the sequence is arithmetic.
All terms except for the fourth term follow this therefore, the sequence is neither arithmetic nor geometric.
To identify the sequence as either arithmetic or geometric, first recall the difference between the two. An arithmetic sequence means there exists a common difference between the terms. If a sequence is geometric, then there exists a common ratio between the terms.
Looking at the given sequence,
subtract the first term from the second term to find the common difference.
From here, add the common difference to the second term.
If adding the common difference to each term in the sequence results in next term then the sequence is arithmetic.
All terms except for the fourth term follow this therefore, the sequence is neither arithmetic nor geometric.
Compare your answer with the correct one above
Identify the following sequence as arithmetic, geometric, or neither.
Identify the following sequence as arithmetic, geometric, or neither.
To identify the sequence as either arithmetic or geometric, first recall the difference between the two. An arithmetic sequence means there exists a common difference between the terms. If a sequence is geometric, then there exists a common ratio between the terms.
Looking at the given sequence,
subtract the first term from the second term to find the common difference.
From here, add the common difference to the second term. If the sum is the third term, then the sequence is arithmetic.
If adding the common difference to each term in the sequence results in next term then the sequence is arithmetic.
All terms except for the third term follow this therefore, the sequence is neither arithmetic nor geometric.
To identify the sequence as either arithmetic or geometric, first recall the difference between the two. An arithmetic sequence means there exists a common difference between the terms. If a sequence is geometric, then there exists a common ratio between the terms.
Looking at the given sequence,
subtract the first term from the second term to find the common difference.
From here, add the common difference to the second term. If the sum is the third term, then the sequence is arithmetic.
If adding the common difference to each term in the sequence results in next term then the sequence is arithmetic.
All terms except for the third term follow this therefore, the sequence is neither arithmetic nor geometric.
Compare your answer with the correct one above
Identify the following sequence as arithmetic, geometric, or neither.
Identify the following sequence as arithmetic, geometric, or neither.
To identify the sequence as either arithmetic or geometric, first recall the difference between the two. An arithmetic sequence means there exists a common difference between the terms. If a sequence is geometric, then there exists a common ratio between the terms.
Looking at the given sequence,
subtract the first term from the second term to find the common difference.
From here, add the common difference to the second term. If the sum is the third term, then the sequence is arithmetic.
If adding the common difference to each term in the sequence results in next term then the sequence is arithmetic.
All terms except for the third term follow this therefore, the sequence is neither arithmetic nor geometric.
To identify the sequence as either arithmetic or geometric, first recall the difference between the two. An arithmetic sequence means there exists a common difference between the terms. If a sequence is geometric, then there exists a common ratio between the terms.
Looking at the given sequence,
subtract the first term from the second term to find the common difference.
From here, add the common difference to the second term. If the sum is the third term, then the sequence is arithmetic.
If adding the common difference to each term in the sequence results in next term then the sequence is arithmetic.
All terms except for the third term follow this therefore, the sequence is neither arithmetic nor geometric.
Compare your answer with the correct one above
Identify the following sequence as arithmetic, geometric, or neither.
Identify the following sequence as arithmetic, geometric, or neither.
To identify the sequence as either arithmetic or geometric, first recall the difference between the two. An arithmetic sequence means there exists a common difference between the terms. If a sequence is geometric, then there exists a common ratio between the terms.
Looking at the given sequence,
divide the second term by the first term to find the common ratio.
From here, multiply the common ratio by each term to get the next term in the sequence.
Since each term is found by multiplying the common ratio with the previous term, the sequence is known as a geometric one.
To identify the sequence as either arithmetic or geometric, first recall the difference between the two. An arithmetic sequence means there exists a common difference between the terms. If a sequence is geometric, then there exists a common ratio between the terms.
Looking at the given sequence,
divide the second term by the first term to find the common ratio.
From here, multiply the common ratio by each term to get the next term in the sequence.
Since each term is found by multiplying the common ratio with the previous term, the sequence is known as a geometric one.
Compare your answer with the correct one above
Identify the following sequence as arithmetic, geometric, or neither.
Identify the following sequence as arithmetic, geometric, or neither.
To identify the sequence as either arithmetic or geometric, first recall the difference between the two. An arithmetic sequence means there exists a common difference between the terms. If a sequence is geometric, then there exists a common ratio between the terms.
Looking at the given sequence,
divide the second term by the first term to find the common ratio.
From here, multiply the common ratio by each term to get the next term in the sequence.
Since each term is found by multiplying the common ratio with the previous term, the sequence is known as a geometric one.
To identify the sequence as either arithmetic or geometric, first recall the difference between the two. An arithmetic sequence means there exists a common difference between the terms. If a sequence is geometric, then there exists a common ratio between the terms.
Looking at the given sequence,
divide the second term by the first term to find the common ratio.
From here, multiply the common ratio by each term to get the next term in the sequence.
Since each term is found by multiplying the common ratio with the previous term, the sequence is known as a geometric one.
Compare your answer with the correct one above
Identify the following sequence as arithmetic, geometric, or neither.
Identify the following sequence as arithmetic, geometric, or neither.
To identify the sequence as either arithmetic or geometric, first recall the difference between the two. An arithmetic sequence means there exists a common difference between the terms. If a sequence is geometric, then there exists a common ratio between the terms.
Looking at the given sequence,
divide the second term by the first term to find the common ratio.
From here, multiply the common ratio by each term to get the next term in the sequence.
Since each term is found by multiplying the common ratio with the previous term, the sequence is known as a geometric one.
To identify the sequence as either arithmetic or geometric, first recall the difference between the two. An arithmetic sequence means there exists a common difference between the terms. If a sequence is geometric, then there exists a common ratio between the terms.
Looking at the given sequence,
divide the second term by the first term to find the common ratio.
From here, multiply the common ratio by each term to get the next term in the sequence.
Since each term is found by multiplying the common ratio with the previous term, the sequence is known as a geometric one.
Compare your answer with the correct one above
Identify the following series as arithmetic, geometric, or neither.
100, 200, 300, 400, 500...
Identify the following series as arithmetic, geometric, or neither.
100, 200, 300, 400, 500...
This is an arithmetic sequence. Note that the same number (100) is added to each value in the set to give us our next number:
100
100 + 100 = 200
200 + 100 = 300
300 + 100 = 400
400 + 100 = 500
When the same value is added to each term to determine the next one, that is an arithmetic sequence.
This is an arithmetic sequence. Note that the same number (100) is added to each value in the set to give us our next number:
100
100 + 100 = 200
200 + 100 = 300
300 + 100 = 400
400 + 100 = 500
When the same value is added to each term to determine the next one, that is an arithmetic sequence.
Compare your answer with the correct one above
1, 9, 81, 729, 6561...
Is the sequence above arithmetic, geometric, or neither?
1, 9, 81, 729, 6561...
Is the sequence above arithmetic, geometric, or neither?
The series is geometric, which means that to get from one value to the next you always multiply by the same value. Here to get from one value to the next, you multiply by 9 each time:
1 x 9 = 9
9 x 9 = 81
81 x 9 = 729
729 x 9 = 6561
The series is geometric, which means that to get from one value to the next you always multiply by the same value. Here to get from one value to the next, you multiply by 9 each time:
1 x 9 = 9
9 x 9 = 81
81 x 9 = 729
729 x 9 = 6561
Compare your answer with the correct one above
What type of sequence describes the following set of numbers?
3, 15, 75, 375, 1875
What type of sequence describes the following set of numbers?
3, 15, 75, 375, 1875
This is a geometric series. The same value, 5, is multiplied by each value to get to the next:
3 x 5 = 15
15 x 5 = 75
75 x 5 = 375
375 x 5 = 1875
When each term in a series is equal to the previous term multiplied by the same factor - in this case 5 - that's a geometric series.
This is a geometric series. The same value, 5, is multiplied by each value to get to the next:
3 x 5 = 15
15 x 5 = 75
75 x 5 = 375
375 x 5 = 1875
When each term in a series is equal to the previous term multiplied by the same factor - in this case 5 - that's a geometric series.
Compare your answer with the correct one above
Identify the following series as arithmetic, geometric, or neither.
100, 200, 300, 400, 500...
Identify the following series as arithmetic, geometric, or neither.
100, 200, 300, 400, 500...
This is an arithmetic sequence. Note that the same number (100) is added to each value in the set to give us our next number:
100
100 + 100 = 200
200 + 100 = 300
300 + 100 = 400
400 + 100 = 500
When the same value is added to each term to determine the next one, that is an arithmetic sequence.
This is an arithmetic sequence. Note that the same number (100) is added to each value in the set to give us our next number:
100
100 + 100 = 200
200 + 100 = 300
300 + 100 = 400
400 + 100 = 500
When the same value is added to each term to determine the next one, that is an arithmetic sequence.
Compare your answer with the correct one above
1, 9, 81, 729, 6561...
Is the sequence above arithmetic, geometric, or neither?
1, 9, 81, 729, 6561...
Is the sequence above arithmetic, geometric, or neither?
The series is geometric, which means that to get from one value to the next you always multiply by the same value. Here to get from one value to the next, you multiply by 9 each time:
1 x 9 = 9
9 x 9 = 81
81 x 9 = 729
729 x 9 = 6561
The series is geometric, which means that to get from one value to the next you always multiply by the same value. Here to get from one value to the next, you multiply by 9 each time:
1 x 9 = 9
9 x 9 = 81
81 x 9 = 729
729 x 9 = 6561
Compare your answer with the correct one above
What type of sequence describes the following set of numbers?
3, 15, 75, 375, 1875
What type of sequence describes the following set of numbers?
3, 15, 75, 375, 1875
This is a geometric series. The same value, 5, is multiplied by each value to get to the next:
3 x 5 = 15
15 x 5 = 75
75 x 5 = 375
375 x 5 = 1875
When each term in a series is equal to the previous term multiplied by the same factor - in this case 5 - that's a geometric series.
This is a geometric series. The same value, 5, is multiplied by each value to get to the next:
3 x 5 = 15
15 x 5 = 75
75 x 5 = 375
375 x 5 = 1875
When each term in a series is equal to the previous term multiplied by the same factor - in this case 5 - that's a geometric series.
Compare your answer with the correct one above
Identify the following sequence as arithmetic, geometric, or neither.
Identify the following sequence as arithmetic, geometric, or neither.
To identify the sequence as either arithmetic or geometric, first recall the difference between the two. An arithmetic sequence means that there is a common difference between the terms. If a sequence is geometric, then there is a common ratio between the terms.
Looking at the given sequence,
subtract the first term from the second term to find the common difference.
From here, add the common difference to the second term. If the sum is the third term, then the sequence is arithmetic.
Adding the common difference to each term in the sequence results in the next term in the sequence which makes this particular sequence, arithmetic.
To identify the sequence as either arithmetic or geometric, first recall the difference between the two. An arithmetic sequence means that there is a common difference between the terms. If a sequence is geometric, then there is a common ratio between the terms.
Looking at the given sequence,
subtract the first term from the second term to find the common difference.
From here, add the common difference to the second term. If the sum is the third term, then the sequence is arithmetic.
Adding the common difference to each term in the sequence results in the next term in the sequence which makes this particular sequence, arithmetic.
Compare your answer with the correct one above
Identify the following sequence as arithmetic, geometric, or neither.
Identify the following sequence as arithmetic, geometric, or neither.
To identify the sequence as either arithmetic or geometric, first recall the difference between the two. An arithmetic sequence means there exists a common difference between the terms. If a sequence is geometric, then there exists a common ratio between the terms.
Looking at the given sequence,
subtract the first term from the second term to find the common difference.
From here, add the common difference to the second term. If the sum is the third term, then the sequence is arithmetic.
Adding the common difference to each term in the sequence results in the next term in the sequence which makes this particular sequence, arithmetic.
To identify the sequence as either arithmetic or geometric, first recall the difference between the two. An arithmetic sequence means there exists a common difference between the terms. If a sequence is geometric, then there exists a common ratio between the terms.
Looking at the given sequence,
subtract the first term from the second term to find the common difference.
From here, add the common difference to the second term. If the sum is the third term, then the sequence is arithmetic.
Adding the common difference to each term in the sequence results in the next term in the sequence which makes this particular sequence, arithmetic.
Compare your answer with the correct one above
Identify the following sequence as arithmetic, geometric, or neither.
Identify the following sequence as arithmetic, geometric, or neither.
To identify the sequence as either arithmetic or geometric, first recall the difference between the two. An arithmetic sequence means there exists a common difference between the terms. If a sequence is geometric, then there exists a common ratio between the terms.
Looking at the given sequence,
subtract the first term from the second term to find the common difference.
From here, add the common difference to the second term. If the sum is the third term, then the sequence is arithmetic.
Adding the common difference to each term in the sequence results in the next term in the sequence which makes this particular sequence, arithmetic.
To identify the sequence as either arithmetic or geometric, first recall the difference between the two. An arithmetic sequence means there exists a common difference between the terms. If a sequence is geometric, then there exists a common ratio between the terms.
Looking at the given sequence,
subtract the first term from the second term to find the common difference.
From here, add the common difference to the second term. If the sum is the third term, then the sequence is arithmetic.
Adding the common difference to each term in the sequence results in the next term in the sequence which makes this particular sequence, arithmetic.
Compare your answer with the correct one above
Identify the following sequence as arithmetic, geometric, or neither.
Identify the following sequence as arithmetic, geometric, or neither.
To identify the sequence as either arithmetic or geometric, first recall the difference between the two. An arithmetic sequence means there exists a common difference between the terms. If a sequence is geometric, then there exists a common ratio between the terms.
Looking at the given sequence,
subtract the first term from the second term to find the common difference.
From here, add the common difference to the second term.
If adding the common difference to each term in the sequence results in next term then the sequence is arithmetic.
All terms except for the fourth term follow this therefore, the sequence is neither arithmetic nor geometric.
To identify the sequence as either arithmetic or geometric, first recall the difference between the two. An arithmetic sequence means there exists a common difference between the terms. If a sequence is geometric, then there exists a common ratio between the terms.
Looking at the given sequence,
subtract the first term from the second term to find the common difference.
From here, add the common difference to the second term.
If adding the common difference to each term in the sequence results in next term then the sequence is arithmetic.
All terms except for the fourth term follow this therefore, the sequence is neither arithmetic nor geometric.
Compare your answer with the correct one above
Identify the following sequence as arithmetic, geometric, or neither.
Identify the following sequence as arithmetic, geometric, or neither.
To identify the sequence as either arithmetic or geometric, first recall the difference between the two. An arithmetic sequence means there exists a common difference between the terms. If a sequence is geometric, then there exists a common ratio between the terms.
Looking at the given sequence,
subtract the first term from the second term to find the common difference.
From here, add the common difference to the second term. If the sum is the third term, then the sequence is arithmetic.
If adding the common difference to each term in the sequence results in next term then the sequence is arithmetic.
All terms except for the third term follow this therefore, the sequence is neither arithmetic nor geometric.
To identify the sequence as either arithmetic or geometric, first recall the difference between the two. An arithmetic sequence means there exists a common difference between the terms. If a sequence is geometric, then there exists a common ratio between the terms.
Looking at the given sequence,
subtract the first term from the second term to find the common difference.
From here, add the common difference to the second term. If the sum is the third term, then the sequence is arithmetic.
If adding the common difference to each term in the sequence results in next term then the sequence is arithmetic.
All terms except for the third term follow this therefore, the sequence is neither arithmetic nor geometric.
Compare your answer with the correct one above