What is the sum of the geometric sequence -3, 18, -108, … if there are 7 terms?

3 Answers
Aug 14, 2018

S_7=-119973

Explanation:

"the sum to n terms for a geometric sequence is"

•color(white)(x)S_n=(a(r^(n-1)))/(r-1)

"where a is the first term and r the common ratio"

a=-3" and "r=(-108)/18=18/(-3)=-6

S_7=(-3((-6)^7-1))/(-6-1)

color(white)(xx)=(-3(-279936-1))/(-7)

color(white)(xx)=(-3xx-279937)/(-7)=-19973

Aug 14, 2018

S_7=-119973

Explanation:

Here,

-3,18,-108,..."are in GP"

Let ,first term =a_1=-3 and

common ratio =r=(-108)/18=18/(-3)=-6

So, the sum of first n terms is:

S_n=(a_1(1-r^n))/(1-r) ,where, n=7

:S_7=(-3(1-(-6)^7))/(1-(-6))

:.S_7=-(3(1+279936))/7=-(3(279937))/7=-119973

Aug 14, 2018

-119973

Explanation:

We can first see that the ratio between these is -6. This means we have the sum of a geometric series, which we know is
S_n = a_1 * (r^n-1)/(r-1) = -3 * ((-6)^7 - 1)/((-6)-1) = -119973