Question

Here are the first four terms of a sequence.

7
12
17
22
Write an expression for the nth term of this sequence

Answer 1

`\mbox{\large a_n = 2 + 5n}`

Explanation:

The sequence is 7 12 17 22

This is an arithmetic sequence where any two successive terms is a constant known as the common difference

The difference between any two successive terms is 5

The common difference is 5

The nth term can be found by the expression

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

where

`a_n \textrm{ is the $n^(th)$ term}`

`\mathrm{a_1\;is\;the\;first\;term}`

`\mathrm{d\;is\;the\;common\;difference}\\`

In this sequence

`a_1 = 7\\d = 5\\`

`a_n = 7 + 5(n-1)\\\\a_n = 7 + 5n - 5\\\\a_n = 2 + 5n`

We can verify that this is correct is to determine the 5th term of the sequence which should be 22 + 5 = 27

Applying the expression for 5th term

`a_5 = 2 + 5(5)\\= 2 + 25\\= 27`