Question

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

Answer 1

`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`

Answer 2

`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`

Answer 3

-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`