# What is the sum of the geometric sequence 1, 3, 9, ... if there are 11 terms?

**Solution:**

The formula to find the sum of geometric sequence is

a(r^{n} - 1)/ (r - 1)

Where a is the first number

r is the common ratio

n is the number of terms

It is given that

a = 1

r = 3/1 = 3

n = 11

Substituting it in the formula

Sum of the geometric sequence = a(r^{n} - 1)/ (r - 1)

= 1 (3^{11} - 1)/ (3 - 1)

By further calculation

= 1 (177147 - 1)/ 2

= 177146/ 2

So we get

= 88573

Therefore, the sum of the geometric sequence is 88573.

## What is the sum of the geometric sequence 1, 3, 9, ... if there are 11 terms?

**Summary:**

The sum of the geometric sequence 1, 3, 9, ... if there are 11 terms is 88573.