What is the sum of the geometric sequence 3, 15, 75, … if there are 7 terms?

Solution:

The sum of the first n terms of a geometric sequence is given by the expression:

Sn = a(rⁿ - 1)/r - 1

Where

S_n = Sum of the first n terms of the Geometric Ratio

a = First Term of the geometric series

r = common ratio of the geometric series

For the series given in the problem statement

a = 3, r = 5

And S₇ = sum of first 7 terms

S₇ = 3(5⁷ - 1)/5 - 1

= 3(78125 - 1)/4

= 3(78124)/4

= 3(19531)

= 58593

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What is the sum of the geometric sequence 3, 15, 75, … if there are 7 terms?

Summary:

The sum of the geometric sequence 3, 15, 75, … if there are 7 terms is 58593.