# What is the sum of the geometric sequence 3, 15, 75, … if there are 7 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 progression 3, 15, 75, … if there are 7 terms is 58593.

Go through the step-by-step solution to find the sum of 7 terms.

**Explanation:**

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

a = 1st term = 3

r = Common ratio = 5

n = Number of terms = 7

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

⇒ S_{n} = a (1 - r^{n}) / 1 - r

⇒ S_{8} = 3 (1 - 5^{7 }) / 1 - 5

⇒ S_{8}= 3 × (1 - 78125) / ( - 4)

⇒ S_{8}= 3 × ( - 78124) / ( - 4)

⇒ S_{12} = 3 × 19531

⇒ S_{12} = 58593