nth Term of an Arithmetic Sequence - ACT Math
Card 0 of 108
Given the sequence of numbers:
1, 5, 9, _ , _ , 21 ....
What are the two missing terms of the arithmetic sequence?
Given the sequence of numbers:
1, 5, 9, _ , _ , 21 ....
What are the two missing terms of the arithmetic sequence?
The sequence is defined by an = 4_n –_ 3 for such n = 1,2,3,4....
The sequence is defined by an = 4_n –_ 3 for such n = 1,2,3,4....
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What is the next term in the following sequence?
What is the next term in the following sequence?
What is the next term in the following sequence?
This is an arithmetic sequence with a common difference of 
. To find the next term in an arithmetic sequence, add the common difference to the previously listed term:
What is the next term in the following sequence?
This is an arithmetic sequence with a common difference of
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Find the sixth term in the following number sequence.
Find the sixth term in the following number sequence.
This question can be answered by analyzing the sequence provided and determining the pattern. The first term is 
, and the second term is 
The third term is 
Thus, 
has been added to 
in order to obtain 
, and 
has been added to 
in order to obtain 
This shows that 
is added to each preceding term in the sequence in order to obtain the next term. The complete sequence from terms one through six is shown below.
Thus, the sixth term is 
This question can be answered by analyzing the sequence provided and determining the pattern. The first term is
Thus, the sixth term is
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What is the next term of the series 
?
What is the next term of the series
Begin by looking at the transitions from number to number in this series:
From 
to 
: Add 
From 
to 
: Subtract 
From 
to 
: Add 
From 
to 
: Subtract 
From what you can tell, you can guess that the next step will be to add 
. Thus, the next value will be 
.
Begin by looking at the transitions from number to number in this series:
From
From
From
From
From what you can tell, you can guess that the next step will be to add
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What is the next term in the following sequence: 
?
What is the next term in the following sequence:
This sequence is a little tricky. Notice that the second element is equal to the first. After that, the third is equal to the sum of the first two 
, next the fourth is equal to the sum of the second and the third 
, and the same continues for each element after this. Thus, the next element in the series will be equal to 
or 
.
This sequence is a little tricky. Notice that the second element is equal to the first. After that, the third is equal to the sum of the first two
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What is the next term in the sequence?
What is the next term in the sequence?
The difference between each term is constant, thus the sequence is an arithmetic sequence.
Simply find the difference between each term, and add it to the last term to find the next term.
The difference between each term is constant, thus the sequence is an arithmetic sequence.
Simply find the difference between each term, and add it to the last term to find the next term.
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Find the sum of the first fifteen terms in an arithmetic sequence whose sixth term is 
and whose ninth term is 
.
Find the sum of the first fifteen terms in an arithmetic sequence whose sixth term is
Use the formula _a_n = _a_1 + (n – 1)d
_a_6 = a_1 + 5_d
_a_9 = a_1 + 8_d
Subtracting these equations yields
_a_6 – a_9 = –3_d
–7 – 8 = –3_d_
d = 5
_a_1 = 33
Then use the formula for the series; = –30
Use the formula _a_n = _a_1 + (n – 1)d
_a_6 = a_1 + 5_d
_a_9 = a_1 + 8_d
Subtracting these equations yields
_a_6 – a_9 = –3_d
–7 – 8 = –3_d_
d = 5
_a_1 = 33
Then use the formula for the series; = –30
Compare your answer with the correct one above
If the first day of the year is a Monday, what is the 295th day?
If the first day of the year is a Monday, what is the 295th day?
The 295th day would be the day after the 42nd week has completed. 294 days/7 days a week = 42 weeks. The next day would therefore be a monday.
The 295th day would be the day after the 42nd week has completed. 294 days/7 days a week = 42 weeks. The next day would therefore be a monday.
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If the first two terms of a sequence are 
and 
, what is the 38th term?
If the first two terms of a sequence are
The sequence is multiplied by 
each time.
The sequence is multiplied by
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Find the 
term of the following sequence:
Find the
The formula for finding the 
term of an arithmetic sequence is as follows:
where
= the difference between consecutive terms
= the number of terms
Therefore, to find the 
term:
The formula for finding the
where
Therefore, to find the
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What is the 
th term in the following series of numbers: 
?
What is the
Notice that between each of these numbers, there is a difference of 
. This means that for each element, you will add 
. The first element is 
or 
. The second is 
or 
, and so forth... Therefore, for the 
th element, the value will be 
or 
.
Notice that between each of these numbers, there is a difference of
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What is the 
rd term of the following sequence:
?
What is the
Notice that between each of these numbers, there is a difference of 
; however the first number is 
, the second 
, and so forth. This means that for each element, you know that the value must be 
, where 
is that number's place in the sequence. Thus, for the 
rd element, you know that the value will be 
or 
.
Notice that between each of these numbers, there is a difference of
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Given the sequence of numbers:
1, 5, 9, _ , _ , 21 ....
What are the two missing terms of the arithmetic sequence?
Given the sequence of numbers:
1, 5, 9, _ , _ , 21 ....
What are the two missing terms of the arithmetic sequence?
The sequence is defined by an = 4_n –_ 3 for such n = 1,2,3,4....
The sequence is defined by an = 4_n –_ 3 for such n = 1,2,3,4....
Compare your answer with the correct one above
What is the next term in the following sequence?
What is the next term in the following sequence?
What is the next term in the following sequence?
This is an arithmetic sequence with a common difference of . To find the next term in an arithmetic sequence, add the common difference to the previously listed term:
What is the next term in the following sequence?
This is an arithmetic sequence with a common difference of
Compare your answer with the correct one above
Find the sixth term in the following number sequence.
Find the sixth term in the following number sequence.
This question can be answered by analyzing the sequence provided and determining the pattern. The first term is , and the second term is The third term is Thus, has been added to in order to obtain , and has been added to in order to obtain This shows that is added to each preceding term in the sequence in order to obtain the next term. The complete sequence from terms one through six is shown below.
Thus, the sixth term is
This question can be answered by analyzing the sequence provided and determining the pattern. The first term is
Thus, the sixth term is
Compare your answer with the correct one above
What is the next term of the series ?
What is the next term of the series
Begin by looking at the transitions from number to number in this series:
From to : Add
From to : Subtract
From to : Add
From to : Subtract
From what you can tell, you can guess that the next step will be to add . Thus, the next value will be .
Begin by looking at the transitions from number to number in this series:
From
From
From
From
From what you can tell, you can guess that the next step will be to add
Compare your answer with the correct one above
What is the next term in the following sequence: ?
What is the next term in the following sequence:
This sequence is a little tricky. Notice that the second element is equal to the first. After that, the third is equal to the sum of the first two , next the fourth is equal to the sum of the second and the third , and the same continues for each element after this. Thus, the next element in the series will be equal to or .
This sequence is a little tricky. Notice that the second element is equal to the first. After that, the third is equal to the sum of the first two
Compare your answer with the correct one above
What is the next term in the sequence?
What is the next term in the sequence?
The difference between each term is constant, thus the sequence is an arithmetic sequence.
Simply find the difference between each term, and add it to the last term to find the next term.
The difference between each term is constant, thus the sequence is an arithmetic sequence.
Simply find the difference between each term, and add it to the last term to find the next term.
Compare your answer with the correct one above
Find the sum of the first fifteen terms in an arithmetic sequence whose sixth term is and whose ninth term is .
Find the sum of the first fifteen terms in an arithmetic sequence whose sixth term is
Use the formula _a_n = _a_1 + (n – 1)d
_a_6 = a_1 + 5_d
_a_9 = a_1 + 8_d
Subtracting these equations yields
_a_6 – a_9 = –3_d
–7 – 8 = –3_d_
d = 5
_a_1 = 33
Then use the formula for the series; = –30
Use the formula _a_n = _a_1 + (n – 1)d
_a_6 = a_1 + 5_d
_a_9 = a_1 + 8_d
Subtracting these equations yields
_a_6 – a_9 = –3_d
–7 – 8 = –3_d_
d = 5
_a_1 = 33
Then use the formula for the series; = –30
Compare your answer with the correct one above
If the first day of the year is a Monday, what is the 295th day?
If the first day of the year is a Monday, what is the 295th day?
The 295th day would be the day after the 42nd week has completed. 294 days/7 days a week = 42 weeks. The next day would therefore be a monday.
The 295th day would be the day after the 42nd week has completed. 294 days/7 days a week = 42 weeks. The next day would therefore be a monday.
Compare your answer with the correct one above