What is the sum of the geometric sequence -3, 18, -108, ... if there are 7 terms?

Solution:

It is given that the geometric sequence -3, 18, -108, ...

Number of the terms (n) = 7

First term (a) = -3

Common ratio = 18/-3 = -6

Since, the common ratio < 1.

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

S_n = a(1 - rⁿ)/(1 - r)

Substituting the values

S₇ = -3[1 - (-6)⁷]/[1 + 6]

By further calculation,

S₇ = -3[1 + 279936]/[7]

S₇ = -3[279937]/[7]

So we get,

S₇ = -3 × 39991

S₇ = -119973

Therefore, the sum of the geometric sequence is S₇ = -119973.

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What is the sum of the geometric sequence -3, 18, -108, ... if there are 7 terms?

Summary:

The sum of the geometric sequence -3, 18, -108, ... if there are 7 terms is S₇ = -119973.