Question

Write an equation to describe the sequence below. Use n to represent the position of a term in the sequence,where n = 1 for the first term.

5, -3 , 9/5 , ...

Write your answer using proper fractions, improper fractions, and integers.

an =
`( )^(n-1)`n - 1

Answer 1

2,2

Explanation:

Answer 2

The required equation is:

`a_n=5( - (3)/(5) )^(n-1)`

EXPLANATION

The given sequence is

`5, -3 , (9)/(5)`

The first term of the sequence is ;

`a_1=5`

The common ratio is the subsequent term previous term of any two consecutive terms. This implies that;

`r = ( - 3)/(5)`

The nth term of the sequence is

`a_n=a_1(r)^(n-1)`

We substitute the terms to obtain;

`a_n=5( - (3)/(5) )^(n-1)`