Question

Use the formula an = aj(r)a- to write a formula for the geometric sequence below.

3, 6, 12, 24, 48, ...

Answer 1

`a_(n)` = 3
`(2)^(n-1)`

Explanation:

There is a common ratio r between consecutive terms in the sequence, that is

6 ÷ 3 = 12 ÷ 6 = 24 ÷ 12 = 48 ÷ 24 = 2

This indicates the sequence is geometric with n th term

`a_(n)` = a₁
`(r)^(n-1)`

where a₁ is the first term and r the common ratio

Here a₁ = 3 and r = 2 , thus

`a_(n)` = 3
`(2)^(n-1)`