Question

These are the first six terms of a sequence with a = 2:

2, 18, 162, 1458, 13122, 118098, ...
Find a recursive formula for this sequence that is valid for n > 1.
Write your answer in simplest form.

Answer 1

`a_(n)` = 9
`a_(n-1)`

Explanation:

Note there is a common ratio r between consecutive terms of the sequence, that is

r = 18 ÷ 2 = 162 ÷ 18 = 1458 ÷ 162 = 13122 ÷ 1458 = 9

A recursive formula allows a term in the sequence to be found by multiplying the previous term by the common ratio, that is

`a_(n)` = 9
`a_(n-1)` with a₁ = 2