What is the 7th term of the geometric sequence 4, -20, 100, …?

Solution:

A geometric series is the sum of finite or infinite terms of a geometric sequence.

For the geometric sequence a, ar, ar², ..., ar^n-1, ..., the corresponding geometric series is a + ar + ar² + ..., ar^n-1 + ....

The geometric series given as 4, -20, 100…..

First term = 4

Common ratio = -20/4 = -5

Tn = ar^{n - 1}

T₇ = ar^{7 - 1} = 4 × (-5)^{7 - 1} = 4 × (-5)⁶ = 62500

The seventh term is 62500

What is the 7th term of the geometric sequence 4, -20, 100, …?

Summary:

The 7th term of the geometric sequence 4, -20, 100, … is 62500