Question

What is the 6th term of the geometric sequence 4, −20, 100, ...?

Answer 1

Let's calculate r of this G.P: (-20)/(4) = - 5(100)/(-20) = - 5So r = -5
The formula to find the nth term of a GP is;
a(n) = a(r)ⁿ⁻¹
a₆ = a(r)⁶⁻¹
a₆ = 4(-5)⁵ = -12500

Answer 2

the 6th term of the given sequence is, - 12500

Explanation:

The nth term for the geometric sequence is given by:

`a_n = a_1 \cdot r^(n-1)` ....[1]

where,

`a_1` is the first term

r is the common ratio of the terms.

Given the sequence:

4, −20, 100, ...

This is a geometric sequence.

Here,

`a_1 =4` and r = -5

We have to find the 6th term of the given sequence:

Substitute n= 6 and the given values in [1] we have;

`a_6 = 4 \cdot (-5)^5 = 4 \cdot -3125 = -12500`

therefore, the 6th term of the given sequence is, - 12500