What is the sum of the geometric sequence 1, 4, 16, … if there are 8 terms?

Solution:

It is given that the geometric sequence 1, 4, 16, …

Number of the terms (n) = 8

First term (a) = 1

Common ratio = 4/1 = 4

Since, the common ratio < 1.

Formula to calculate the sum of the G.P. will be given by the relation,

Sn = a(rⁿ - 1)/(r - 1)

Substituting the values

S₈ = 1[(4)⁸ - 1]/[4 - 1]

By further calculation

S₈ = 1[65536 - 1]/[3]

So we get,

S₈ = 65535/3

S₈ = 21845

Therefore, the sum is S₈ = 21845.

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What is the sum of the geometric sequence 1, 4, 16, … if there are 8 terms?

Summary:

The sum of the geometric sequence 1, 4, 16, … if there are 8 terms is S₈ = 21845.