What is the sum of the geometric sequence 3, 15, 75, … if there are 8 terms?

Solution:

Sum of n terms of geometric progression :

S_n = a(1 - rⁿ)/(1 - r)

Given geometric sequence is:

3, 15, 75, …

Here,

a = 3,

r = 15/3 = 5,

n = 8

S_n = a(1 - rⁿ)/(1 - r)

S₈ = 3(1 - 5⁸)/(1 - 5)

S₈ = 3 × (1 - 46656)/(-4)

S₈ = 3 × (1-390625)/(-4)

S₈ = 292968

Therefore, the sum of the geometric sequence is S₈ = 292968.

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What is the sum of the geometric sequence 3, 15, 75, … if there are 8 terms?

Summary:

The sum of the geometric sequence 3, 15, 75, …, if there are 8 terms, is S₈ = 292968.