How to find the common difference in sequences - SSAT Upper Level Quantitative

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.

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:

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 .

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 .

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 .

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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