Question

Write a rule for the nth term of the arithmetic sequence. d =1/2 , a6 =18.

Answer 1

`a_(n)` =
`(1)/(2)` n + 15

Explanation:

The n th term of an arithmetic sequence is

`a_(n)` = a₁ + (n - 1)d

where a₁ is the first term and d the common difference

Given a₆ = 18 and d =
`(1)/(2)` , then

a₁ + 5d = 18 , that is

a₁ +
`(5)/(2)` = 18 ( subtract
`(5)/(2)` from both sides )

a₁ =
`(31)/(2)`

Thus

`a_(n)` =
`(31)/(2)` +
`(1)/(2)` (n - 1) =
`(15)/(2)` +
`(1)/(2)` n -
`(1)/(2)` =
`(1)/(2)` n + 15