Question

Please help with this

Answer 1

`S_(n)` = n² + 4n ; n = 11

Explanation:

`S_(n)` =
`(n)/(2)` [2
`a_(1)` + (n - 1)d]

~~~~~~~~~

`a_(1)` = 5

d = 7 - 5 = 2

`S_(n)` =
`(n)/(2)` [ 2(5) + 2(n - 1)] =
`(n)/(2)` ( 8 + 2n ) = 4n + n²

`S_(n)` = n² + 4n

n² + 4n = 165

n² + 4n - 165 = 0

(n + 15)(n - 11) = 0 ( n ≥ 0 ) ⇒ n = 11