What is the sum of the geometric sequence 2, 10, 50, … if there are 7 terms?

Solution:

Sum of the geometric sequence is:

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

Given:

Series is 2, 10, 50,.... Upto 7 terms.

First term of the series a 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 = 7

⇒ S₇ = 2 (5⁷ - 1) / (5 - 1)

⇒ S₇ = 2 (78125 - 1) / 4

⇒ S₇ = 2 (78124) / 4

⇒ S₇ = 156248 / 4

⇒ S₇ = 39062

Therefore , the sum is 39062.

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What is the sum of the geometric sequence 2, 10, 50, … if there are 7 terms?

Summary:

The sum of the geometric sequence 2, 10, 50, … if there are 7 terms is 39062.