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

Solution:

Sum of the geometric sequence is :

S = a + ar + ar¹ + ar² +....+ ar^{n - 1}

First term of the series is 2.

Common ratio is r.

To find r,

r = 10/2

r = 5

Since r > 1, sum of geometric sequence can be found by using the relation,

S_n = a(rⁿ - 1) / (r - 1), r ≠ 1

Given, n = 8

S = 2 ((5)⁸ - 1) / (5 - 1)

S = 2(390625 - 1) / 4

S = (390624) / 2

S = 195312

Therefore , the sum of geometric sequence 2,10,50...upto 8 terms is 195312.

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

Summary:

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