Question

Given the folowing sequence of numbers find the recursive formula, and the appropriate sequenceformula, (arithmetic or geometric) 6, -12, 24, -48

Answer 1

The given sequence is

6, -12, 24, -48

in a geometric sequence, the consecutive terms are related by a common ratio. each term is determined by multiplying the term before it by a common ratio. looking at the given sequence,

- 12/6 = 24/- 12 = - 48/24 = - 2

The common ratio is - 2. thus, it is a geometric sequence. To write the recursive formula, we would make use of the first term. The first term is - 2.

If there are n terms, the term before the last term is n - 1

The first term is a1

The nth term is

`a_{n\text{ - 1}}`

The recursive formula would be

`a_n=a_{\text{n -1}}\text{ }*-\text{ 2}`