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Example Questions
Example Question #1691 : Act Math
Find the sum of the first fifteen terms in an arithmetic sequence whose sixth term is 
Use the formula an = a1 + (n – 1)d
a6 = a1 + 5d
a9 = a1 + 8d
Subtracting these equations yields
a6 – a9 = –3d
–7 – 8 = –3d
d = 5
a1 = 33
Then use the formula for the series; = –30
Example Question #1 : How To Find The Next Term In An Arithmetic Sequence
Given the sequence of numbers:
1, 5, 9, _ , _ , 21 ....
What are the two missing terms of the arithmetic sequence?
12, 18
14, 16
13, 16
13, 17
14, 17
13, 17
The sequence is defined by an = 4n – 3 for such n = 1,2,3,4....
Example Question #1692 : Act Math
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 
Example Question #1 : How To Find The Next Term In An Arithmetic 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 
Thus, the sixth term is 
Example Question #3 : How To Find The Next Term In An Arithmetic Sequence
What is the next term of the series 
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 
Example Question #2 : How To Find The Next Term In An Arithmetic 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 
Example Question #1 : How To Find The Next Term In An Arithmetic 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.
Example Question #1 : How To Find The Missing Number In A Set
Ryan’s class lined up in order of birthdays. If Ryan is the 11th oldest and 9th youngest, how many students are in his class?
18
21
11
20
19
19
Ryan is the 11th oldest and 9th youngest, so there are 10 students older than him and 8 younger than him. The 10 older plus the 8 younger plus Ryan himself gives a total of 10+8+1 = 19. (The trick is not to double-count Ryan.)
Example Question #2 : How To Find The Missing Number In A Set
What is the next integer in this series of numbers?
1, 4, 7, 10, 13, ?
16
17
15
14
18
16
Each number is the previous number + 3.
Example: 1 + 3 = 4
13+3 = 16
Example Question #2 : How To Find The Missing Number In A Set
If the average and median of the group of integers shown below is equal to x, what is the value of x?
40, 11, 62, x, 20, 51, 2
28
31
26
14
31
First, we must find the average of these 6 numbers. This is done by adding all of them and dividing by the number of values we have (in this case, 6).
Next, we have to make sure that this number is also the median. Since the median is the middle number of our values put in ascending order, we have to put our values in increasing order:
2, 11, 20, 31, 40, 51, 62
When we do this, we see that 31 is indeed the “middle number” so we are happy with choosing 31 as our correct answer
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