Question

What is the sum of the geometric series?

Answer 1

40

Explanation:

we need the sum of the first 4 terms of this GS

= (-2)(-3)^0 + (-2)(-3)^(2-1) + (-2)(-3)^(3-1) + (-2)(-3)^(4-1)

= -2( 1 + -3 + 9 + -27)

= 2 * -20

= 40

Answer 2

Sum of series is 40.

Explanation:

Given : Geometric series .

To find : Sum of geometric series.

Solution : We have given that ∑
`(-2)(-3)^(n-1)` n = 1 to 4

For n = 1

`S_(1)` =
`(-2)(-3)^(1-1)`

`S_(1)` = (-2)(1)

`S_(1)` = -2.

For n =2

`S_(2)` =
`(-2)(-3)^(2-1)`.

`S_(2)` = 6.

For n =3

`S_(3)` =
`(-2)(-3)^(3-1)`.

`S_(3)` =
`(-2)(-3)^(2)`.

`S_(3)` = (-2)(9).

`S_(3)` = -1.

For n =4

`S_(4)` =
`(-2)(-3)^(4-1)`.

`S_(4)` =
`(-2)(-3)^(3)`.

`S_(4)` =
`(-2)(-27)`.

`S_(4)` = 54.

Sum of all

`S_(1)` +
`S_(2)` +
`S_(3)` +
`S_(4)`.

-2 + 6 + (-18) + 54

-2 +6 -18 +54

4 -18+54

-14+54

40.

Therefore, Sum of series is 40.