Question

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

Answer 1

ANSWER

The 4th term is -27

EXPLANATION

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

$S_n= \frac{n}{2} (2a_1+d(n-1))$

It was given that,

$S_4 = - 36$

$a_1 = 9$

$- 36= \frac{ 4}{2} (2 \times 9+d(4-1))$

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

$-18=18+3d$

$-18 - 18 = 3d$

$3d = - 36$

$d = - 12$

The n-term is given by:

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

We substitute n=4 to get,

$a_4=9+ (4-1) \times -12$

$a_4=9+ 3\times -12$

$a_4=9 - 36$

$a_4= - 27$