Question

What is the sum of the geometric sequence -1, 6, -36, ....if there are 7 terms.

A) -39,991
B) -6,665
C) 6,665
D) 39,991

Answer 1

A) - 39,991

Explanation:

Sum of geometric sequence formula is

`S = a((1 -r^n)/(1-r) )\\a=-1, r=6/(-1)=-6, n=7\\\\S = -1((1 -(-6)^7)/(1-(-6)) )= -(279937)/(7) = -39991`

Answer 2

The correct answer option is A) -39,991.

Explanation:

We know that the sum of the geometric sequence is given by the formula:

`S _ n = \frac { a _ 1 ( 1 - r ^ n ) } { 1 - r }`

where
`a_1` is the first term,
`r` is the common ratio and
`n` is the number of terms.

Here,

`a_1 = -1`

`r = -6`

`n=7`

Substituting these values in the above formula to get:

`S _ 7 = \frac { -1 ( 1 - (-6) ^ 7 ) } { 1 - (-6) }`

S_n = -39,991