How to find the next term in an arithmetic sequence

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SSAT Upper Level Quantitative › How to find the next term in an arithmetic sequence

Questions 1 - 10

1

Find the next term in the following arithmetic sequence:

$\frac{9}{2}, 4, \frac{7}{2}, ?$

$\frac{3}{2}$

$\frac{5}{2}$

Explanation

The common difference for this arithmetic sequence is $-\frac{1}{2}$ . To find the next term in the sequence, subtract that value from the last given value.

$\frac{7}{2}-\frac{1}{2}=3$

2

Find the next term in this arithmetic sequence:

Explanation

The common difference for this sequence is . Subtract from the last given term to find the next term.

3

Find the next term of the arithmetic sequence:

Explanation

The common difference is . Add this to the last given term to find the next term.

4

Find the next term of the arithmetic sequence:

Explanation

The common difference is . Add this to the last given term to find the next term.

5

Find the next term in the following arithmetic sequence:

Explanation

The sequence is subtracting for each term. The next term can be found by subtracting from :

6

Find the next term of the arithmetic sequence:

$-\frac{1}{2}, 3, \frac{13}{2}, ?$

$\frac{19}{2}$

$\frac{17}{2}$

Explanation

The common difference is $\frac{7}{2}$ . Add this to the last given term to find the next term.

$\frac{13}{2}+\frac{7}{2}=\frac{20}{2}=10$

7

Find the next term of the arithmetic sequence:

Explanation

The common difference is . Add this to the last given term to find the next term.

8

Find the next number in this arithmetic sequence:

Explanation

The common difference for this arithmetic sequence is . Take away from to get the next term.

9

Find the next term of this arithmetic sequence:

Explanation

The common difference for this sequence is . Add this to the last given term to find the next one.

10

What is the value of x in the sequence below?

$3\frac{2}{3}$

$11\frac{1}{3}$

$\frac{11}{2}$

Explanation

In this sequence, each subsequent number is equal to one third of the preceding number.

One third of 11 is equal to:

$\frac{11}{3}=3\frac{2}{3}$

Therefore, the correct answer is: $3\frac{2}{3}$

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