How to find the common difference in sequences

SSAT Upper Level Quantitative · Learn by Concept

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

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1

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

Set W, containing multiples of 8.

CORRECT

Set X, containing multiples of 2.

0

Set Y, containing multiples of 6.

0

Set Z, containing multiples of 1.

0

Set Q, containing multiples of 7.

0

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.

2

Find the common difference for the arithmetic sequence:

CORRECT

0

0

0

Explanation

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

3

Find the common difference for the arithmetic sequence:

CORRECT

0

0

0

Explanation

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

4

What number comes next in the sequence?

_______

CORRECT

0

0

0

0

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 .

5

What is the next number in the sequence?

_______

CORRECT

0

0

0

0

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 .

6

Find the common difference for the arithmetic sequence:

CORRECT

0

0

0

Explanation

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

7

Find the common difference for the arithmetic sequence:

CORRECT

0

0

0

Explanation

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

8

Find the common difference for the arithmetic sequence:

CORRECT

0

0

0

Explanation

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

9

Find the common difference for the arithmetic sequence:

CORRECT

0

0

0

Explanation

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

10

What is the next number in the sequence?

_______

CORRECT

0

0

0

0

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 .