Identify the indicated sum for the geometric series. S9 for 3 − 6 + 12 − 24 + ..... ?

1 Answer
Jun 18, 2018

S_9=513

Explanation:

Here,

3,(-6),12,(-24),... is the geometric sequn.

where, 1^(st) term=a_1=3 and common ratio

r= (-6)/3=12/(-6)=(-24)/12=-2 and S_9= ?=>n=9

We know that,

"The sum of first n term of Geometric series is :"

color(blue)(S_n=(a_1(r^n-1))/(r-1)

Putting , a_1=3, r=-2 and n=9

S_9=(3[(-2)^9-1])/((-2)-1)

:.S_9=(3[-512-1])/(-3)

=>S_9=(3(-513))/(-3)

=>S_9=513