# What is the sum of the geometric sequence 1, 3, 9, ... if there are 12 terms?

When the ratio between any two consecutive terms in a sequence is the same, it is called a geometric progression.

## Answer: The sum of the geometric sequence 1, 3, 9, ... if there are 12 terms is 265,720.

Go through the step-by-step solution to find the sum of the given geometric sequence with 12 terms.

**Explanation:**

The general term of any geometric progression = ar^{(n-1)}

a = 1st term = 1

r = common ratio = 3/1 = 9/3 = 3

n = Number of terms = 12

Sum of geometric progression with common ratio r can be calculated using the formula,

⇒ S_{n} = a (1 - r^{n }) / 1 - r

⇒ S_{12} = 1 (1 - 3^{12 }) / 1 - 3

⇒ S_{12}= 1 × (- 531440 ) / (- 2 )

⇒ S_{12} = 1 × 265,720

⇒ S_{12} = 265,720