What is the sum of the geometric sequence 2, 10, 50, … 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 progression 2, 10, 50, … if there are 8 terms is 195312.

Let us go through the step-by-step solution to find the sum of 8 terms.

Explanation:

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

Here,

a = 1st term = 2

r = Common ratio = 5

n = Number of terms = 8

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

⇒ S_n = a (1 - rⁿ) / 1 - r 

⇒ S₈ = 2 (1 - 5⁸) / 1 - 5

⇒ S₈ = 2 × (1 - 390625) / -4

⇒ S₈ = 2 × (-390624) / -4

⇒ S₈ = 2 × 97656

⇒ S₈ = 195312

Thus, the sum of the first 8 terms of the given geometric sequence is 195312.