What is the sum of the geometric sequence -1, 6, -36, ... if there are 7 terms?

Solution:

A geometric progression is a sequence where every term bears a constant ratio to its preceding term. Geometric progression is a special type of sequence.

In order to get the next term in the geometric progression, we have to multiply with a fixed term known as the common ratio, every time, and if we want to find the preceding term in the sequence, we just have to divide the term with the same common ratio.

Here is an example of a geometric progression is 2, 4, 8, 16, 32, ...... having a common ratio of 2

Sum of n terms of geometric progression:

 S_n = a(1 - rⁿ)/(1 - r)

Given, geometric sequence is -1, 6, -36, ...

Here, a = -1, r = 6/-1 = -6, n = 7

S_n = a(1 - rⁿ)/(1 - r)

S₇ = -1(1 - (-6)⁷)/ (1 - (-6))

S₇ = -1(1+279936)/7

S₇ = - 39991

Therefore, the sum of the geometric sequence is S₇ = -39991.

What is the sum of the geometric sequence -1, 6, -36, ... if there are 7 terms?

Summary:

The sum of the geometric sequence -1, 6, -36, ..., if there are 7 terms, is S₇ = -39991.