Question

1) Find the indicated term of the arithmetic sequence with the first term a1 and the common difference d. ?

a. a. Find a7 when a1 = –8 and d = 4.
b. b. Find a16 when a1 = 10 and d = 7.

Answer 1

`color(orange)([a] a_7=16`

`color(orange)([b] a_16=115`

Explanation:

`a]` Find `a_7` when `a_1 = –8` and `d = 4`:

Formula:-

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

So we have, `color(darkred)(=>a_7=(-8)+(7-1)4`

`a_7=(-8)+(6xx4)`

`=>a_7=(-8)+24`

`color(red)(=>a_7=16`

`therefore` The `color(magenta)(7^(th)` term is `color(magenta)(16.`

`b]` Find `a_16` when `a_1 = 10` and `d = 7:`

Formula:-

`color(blue)(=>a_n=a_1+(n-1)d`

So we have, `color(darkred)(a_16=10+(16-1)7`

`=>a_16=10+(15xx7)`

`=>a_16=10+105`

`color(red)(=>a_16 =105`

`therefore`The `color(magenta)(16^(th` term is `color(magenta)(115.`

~Hope this helps! :)