Question

The 4th term of an exponential sequence is 108 and the common ratio is 3. Calculate the value of the eighth term of the sequence.

Answer 1

Answer:

The eighth term is 8748

Step-by-step explanation:

Since the sequence is a geometric sequence

For an nth term in a geometric sequence

$A (n) = a ({r})^{n - 1}$

where

a is the first term

r is the common ratio

n is the number of terms

To find the eighth term we must first find the first term

4th term = 108

common ratio = 3

That's

$A(4) = a ({r})^{4 - 1}$

$108 = a ({3})^{3}$

$27a = 108$

Divide both sides by 27

a = 4

The first term is 4

For the eighth term

$A(8) = 4 ({3})^{8 - 1}$

$A(8) = 4({3})^{7}$

The final answer is

A(8) = 8748

The eighth term is 8748

Hope this helps you