Question

Find a4 for the arithmetic series with S4=-36 and a1=9

Answer 1

-78

Explanation:

Answer 2

The 4th term is -27

EXPLANATION

The sum of the first n-terms of an arithmetic sequence is

`S_n= (n)/(2) (2a_1+d(n-1))`

It was given that,

`S_4 = - 36`

`a_1 = 9`

`- 36= ( 4)/(2) (2 * 9+d(4-1))`

`-36=2(18+3d)`

`-18=18+3d`

`-18 - 18 = 3d`

`3d = - 36`

`d = - 12`

The n-term is given by:

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

We substitute n=4 to get,

`a_4=9+ (4-1) * -12`

`a_4=9+ 3* -12`

`a_4=9 - 36`

`a_4= - 27`