# What is the sum of the first six terms of the geometric series? 2 - 6 + 18 - 54 + …

**Solution:**

In the given geometric series

The first term “a” = 2

The common ratio r = -3

And the sum of n terms of the series is equal to

Sn = a(r^{n} - 1) / (r - 1) I r I > 0

Sn = 6

= (2) [(-3)^{6} - 1] / (-3 - 1)

= (2) [729 - 1] / (-4)

= 728 / (-2)

= -364

**Hence, the required value is - 364.**

## What is the sum of the first six terms of the geometric series?

2 - 6 + 18 - 54 + …

**Summary: **

The sum of the first six terms of the above geometric series is -364.