Question

The 4th term of a sequence is 108. Each term after the first is three times the previous term. Write an expression that represents all 4 terms. Write an equation that represents the 4th term. What are the 4 numbers?

Answer 1

First 4 terms are a, 3a, 3^2 a and 3^3 a.

The numbers are:

4, 12, 36, 108.

Explanation:

This is a geometric sequence and we can write it as:

a, ar, ar^2, ar^3 <---- the first 4 terms.

Here the common ratio r = 3 and the 4th term is 108 so:

a(3)^3 = 108

So the first term a = 108 / 3^3

= 108/27

= 4.

So the second number = 3*4 = 12 and 3rd is 12*3 = 36.