Question

Find the sum of the first 6 terms of 3 - 6 + 12 + …

Answer 1

`S_6 = -63`

Explanation:

The sequence above is a geometric sequence.

The common ratio (r) =
`(-6)/(3) = (12)/(-6) = -2`

The common ratio < 1, therefore, the formula for the sum of nth terms of the sequence would be:
`S_n = (a_1(1 - r^n))/(1 - r)`

a1 = 3

r = -2

n = 6

Plug in the values into the formula

`S_6 = (3(1 - (-2^6))/(1 - (-2))`

`S_6 = (3(1 - (64))/(1 + 2)`

`S_6 = (3(-63))/(3)`

`S_6 = -63`