Question

How do you write a rule for the nth term of the arithmetic sequence given `a_8=12`, `a_15=61`?

Answer 1

The rule for this A.P. is `a_n = 7n-44`

Explanation:

To write a rue for an AP, we need to have the value for the first term,`a_1 and d`, the common difference.

Every term can be written in the general form of an AP,

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

In the terms we have been given we only know the values of `n` and `a_n`

Make 2 equations:

`" "a_8 = a_1 + 7d = 12" ...........................................A`
`" "a_15 = a_1 +14d = 61" .........................................B`

`B - A: " "7d = 49`
`" "d = 7`

Substitute 70 for d in A

`a_1 + 7(7) = 12 " "rArr a_1 = -37`

`a_n = -37 + (n-1)(7)`

`a_n = -37 +7n -7`

The rule for this A.P. is `a_n = 7n-44`