Question

Find the fifth term and the nth term of the geometric sequence whose initial term, a, and common ratio, r, are given.

a = 8; r = -5

Answer 1

Answer:

$a_n = 8(-5)^{n-1}$

The fifth term of the sequence is 5000.

Step-by-step explanation:

Geometric sequence:

In a geometric sequence, the quotient between consecutive terms is always the same, called common ratio. The nth term of a geometric sequence is:

$a_n = a_1(r)^{n-1}$

a = 8; r = -5

Thus:

$a_n = a_1(r)^{n-1}$

$a_n = 8(-5)^{n-1}$

Fifth term:

This is $a_5$. So

$a_5 = 8(-5)^{5-1} = 5000$

The fifth term of the sequence is 5000.