How to find the next term in an arithmetic sequence

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PSAT Math › How to find the next term in an arithmetic sequence

Questions 1 - 4

1

What is the next number in the following series: 0, 3, 8, 15, 24 . . . ?

37

35

40

32

41

Explanation

The series is defined by n2 – 1 starting at n = 1. The sixth number in the series then equal to 62 – 1 = 35.

2

Find the $\small 7th$ term in the sequence

$\small 3 , 7 , 11 , 15 , ...$

$\small 27$

$\small \small \small 23$

$\small 31$

$\small 19$

Explanation

Notice that in the sequence

$\small 3 , 7 , 11 , 15 , ...$

each term increases by $\small 4$ .

It is always good strategy when attempting to find a pattern in a sequence to examine the difference between each term.

We continue the pattern to find:

The $\small 5th$ term is $\small 19$

The $\small \small 6th$ term is $\small \small 23$

The $\small \small \small 7th$ term is $\small \small \small 27$

It is useful to note that the sequence is defined by,

$\small S(n) = 4n -1$

where n is the number of any one term.

We can solve

$\small \small S(7) = 4(7) -1 = 28 - 1 = 27$

to find the $\small 7th$ term.

3

$\small 2, 3, 5, 9, 17, x, 65, 129....$

$\small \textup{In the above number sequence, what is the value of},x?$

$\small 33$

$\small 31$

$\small 32$

$\small 34$

$\small 35$

Explanation

Each term in the sequence is one less than twice the previous term.

So, $\small x=2\left ( 17\right )-1$

$\small x=33$

4

A sequence of numbers is as follows:

What is the sum of the first seven numbers in the sequence?

621

248

1529

490

719

Explanation

The pattern of the sequence is (x+1) * 2.

We have the first 5 terms, so we need terms 6 and 7:

(78+1) * 2 = 158

(158+1) * 2 = 318

3 + 8 + 18 +38 + 78 + 158 + 318 = 621

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