Question

What is the 7th term of the geometric sequence where a1 = 625 and a2 = −125?

Answer 1

Common ratio, r = (-125)/625 = -0.2
First term, a = 625

7 term
= ar^6
= 625(-0.2)^6
= -0.04

Answer 2

The nth term of the geometric sequence is given by;

`a_n = a_1r^(n-1)`, .....[1] n is the number of terms.

where,

`a_1` is the first term and r is the common ratio of the terms.

As per the statement:

Given:

`a_1= 625` and
`a_2 = -125`

Using [1];

`a_2 = a_1 \cdot r`

Substitute the value of
`a_1` we have;

`-125 = 625 \cdot r`

Divide both sides by 625 we have;

`-(1)/(5) = r`

or

`r= -(1)/(5)`

We have to find 7th term of the geometric sequence.

For n = 7 we have;

`a_7 = a_1 \cdot r^6`

Substitute the given values we have;

`a_7 = 625 \cdot (-(1)/(5))^6 = (625)/(15625) = (1)/(25) =0.04`

therefore, the 7th term of the geometric sequence is, 0.04