Question

Formulate the recursive formula for the following geometric sequence. {-16, 4, -1, ...} ?

Answer 1

`a_n=-16(-1/4)^n, n={0,1,2,3,cdots}`

Explanation:

We have the sequence `{-16,4,-1,cdots}`

By looking at the first three terms of the sequence, we can already see a pattern.

Starting at -16, each term has its sign reversed, and is divided by 4.

Hence the sequence can be written as:

`{-16, -16(-1/4), -16(-1/4)^2,cdots}`

So the formula for the `n`th term of the sequence is

`a_n=-16(-1/4)^n, n={0,1,2,3,cdots}`