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

Jul 4, 2017

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.

Jul 4, 2017

From the reference Arithmetic Progression we obtain the following equation:

${a}_{n} = {a}_{1} + d \left(n - 1\right)$

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:

${a}_{n} = 9 + 7 \left(n - 1\right)$

This equation allows us to compute the next 4 terms:

${a}_{4} = 9 + 7 \left(4 - 1\right) = 30$
${a}_{5} = 9 + 7 \left(5 - 1\right) = 37$
${a}_{6} = 9 + 7 \left(6 - 1\right) = 44$
${a}_{7} = 9 + 7 \left(7 - 1\right) = 51$