Question

How do you find the next four terms of the arithmetic sequence 9, 16, 23, ...?

Answer 1

See the explanation below.

Explanation:

In this arithmetic sequence, the common difference `d` is 7. You can find this by subtracting a term from the consecutive term: 16 - 9 = 7, 23 - 16 = 7.

In order to find the next four terms, keep adding 7 to the previous term.

23 + 7 = 30
30 + 7 = 37
37 + 7 = 44
44 + 7 = 51

The next four terms are 30, 37, 44, and 51.

Answer 2

From the reference Arithmetic Progression we obtain the following equation:

`a_n = a_1 + d(n-1)`

where `a_n` is the nth term, `a_1` is the first term, `d` is the difference between each term and `n` is any integer greater than 0.

From the sequence we observe that `a_1 = 9` and `d = 7`; this gives use the following equation:

`a_n = 9 + 7(n-1)`

This equation allows us to compute the next 4 terms:

`a_4 = 9 + 7(4-1) = 30`
`a_5 = 9 + 7(5-1) = 37`
`a_6 = 9 + 7(6-1) = 44`
`a_7 = 9 + 7(7-1) = 51`