# What is the sum of the geometric sequence 4, 16, 64, … if there are 8 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 4, 16, 64, … if there are 8 terms is 87380.

Go through the step-by-step solution to find the sum of 8 terms.

**Explanation:**

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

a = 1^{st }term = 4

r = common ratio = 16/4 = 64/14 = 4

n = Number of terms = 8

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

⇒ S_{n} = a (1 - r^{n }) / 1 - r

⇒ S_{8} = 4 (1 - 4^{8 }) / 1 - 4

⇒ S_{8} = 4 × (- 65535 ) / (- 3)

⇒ S_{8} = 4 × 21845

⇒ S_{8} = 87380