Question

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

Answer 1

Answer:

$S_6 = -63$

Step-by-step explanation:

The sequence above is a geometric sequence.

The common ratio (r) = $\frac{-6}{3} = \frac{12}{-6} = -2$

The common ratio < 1, therefore, the formula for the sum of nth terms of the sequence would be: $S_n = \frac{a_1(1 - r^n)}{1 - r}$

a1 = 3

r = -2

n = 6

Plug in the values into the formula

$S_6 = \frac{3(1 - (-2^6)}{1 - (-2)}$

$S_6 = \frac{3(1 - (64)}{1 + 2}$

$S_6 = \frac{3(-63)}{3}$

$S_6 = -63$