What is the sum of the geometric sequence 2, 8, 32, … if there are 8 terms?

Solution:

The formula to find the sum of geometric sequence is

a(rⁿ - 1)/ (r - 1)

Where a is the first number

r is the common ratio

n is the number of terms

It is given that

a = 2

r = 8/2 = 4

n = 8

Substituting it in the formula

Sum of the geometric sequence = a(rⁿ - 1)/ (r - 1)

= 2 (4⁸ - 1)/ (4 - 1)

By further calculation

= 2 (65536 - 1)/ 3

= 131070/3

So we get

= 43690

Therefore, the sum of the geometric sequence is 43690.

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What is the sum of the geometric sequence 2, 8, 32, … if there are 8 terms?

Summary:

The sum of the geometric sequence 2, 8, 32, … if there are 8 terms is 43690.