SSAT Upper Level Math : How to find the common difference in sequences

Study concepts, example questions & explanations for SSAT Upper Level Math

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Example Questions

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Example Question #1 : How To Find The Common Difference In Sequences

Set R consists of multiples of 4. Which of the following sets are also included within set R?

Possible Answers:

Set X, containing multiples of 2. 

Set Z, containing multiples of 1. 

Set Y, containing multiples of 6. 

Set Q, containing multiples of 7. 

Set W, containing multiples of 8. 

Correct answer:

Set W, containing multiples of 8. 

Explanation:

The easiest way to solve this problem is to write out the first few numbers of the sets. 

Set R (multiples of 4): 

Set W (multiples of 8): 

Set X (multiples of 2): 

Set Y (multiples of 6): 

Set Z (multiples of 1): 

Set Q (multiples of 7): 

Given that Set W is the only set in which the entire set of numbers is reflected in Set R, it is the correct answer. 

Example Question #502 : Number Concepts And Operations

What number comes next in this sequence?

4   12   9   6   18   15   12   36   33   __

Possible Answers:

Correct answer:

Explanation:

Determining sequences can take some trial and error, but generally aren't as intimidating as they may at first appear. For this sequence, you multiply the first term by 3, and then subtract 3 two times in a row. Then repeat. When you get to 33, you have only subtracted 3 once, so you have to do that one more time:

Example Question #2 : How To Find The Common Difference In Sequences

What number comes next in the sequence? 

 _______

Possible Answers:

Correct answer:

Explanation:

In order to find the next number in the sequence, take a look at the patterns and common differences between the existing numbers in the sequence. Starting with , we add  to get , subtract  to get , and then repeat. 

When we get to  for the second time in the sequence, we are adding  to get . By the next step in the sequence, we will subtract  to get the missing number .

Example Question #3 : How To Find The Common Difference In Sequences

What is the next number in the sequence?

 _______

Possible Answers:

Correct answer:

Explanation:

In order to find the next number in the sequence, take a look at the patterns and common differences between the existing numbers in the sequence. Starting with , we add  to get  and then subtract  to get .

By the time we get to , we have subtracted  from  to complete the cycle of common differences. We will therefore add  to  next, getting the missing number .

Example Question #4 : How To Find The Common Difference In Sequences

What is the next number in the sequence?

 _______

Possible Answers:

Correct answer:

Explanation:

In order to find the next number in the sequence, take a look at the patterns and common differences between the existing numbers in the sequence. Starting at the beginning, we multiply  by  to get  and then divide by  to get 

We multiply the second  in the sequence by  to get , so by the logic of the sequence we will be dividing by  to get the missing number .

Example Question #5 : How To Find The Common Difference In Sequences

Find the common difference for the arithmetic sequence:

Possible Answers:

Correct answer:

Explanation:

Subtract the first term from the second term to find the common difference.

Example Question #5 : How To Find The Common Difference In Sequences

Find the common difference for the arithmetic sequence:

Possible Answers:

Correct answer:

Explanation:

Subtract the first term from the second term to find the common difference.

Example Question #6 : How To Find The Common Difference In Sequences

Find the common difference for the arithmetic sequence:

Possible Answers:

Correct answer:

Explanation:

Subtract the first term from the second term to find the common difference.

Example Question #7 : How To Find The Common Difference In Sequences

Find the common difference for the arithmetic sequence:

Possible Answers:

Correct answer:

Explanation:

Subtract the first term from the second term to find the common difference.

Example Question #7 : How To Find The Common Difference In Sequences

Find the common difference for the arithmetic sequence:

Possible Answers:

Correct answer:

Explanation:

Subtract the first term from the second term to find the common difference.

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