Question

Given the functions f(n) = 500 and g(n) = (nine tenths)n − 1, combine them to create a geometric sequence, an, and solve for the 11th term.

Answer 1

`A(n) = 500 * ((9)/(10))^{n-1`

`A(11) = 174.34`

Explanation:

Given

`f(n) = 500`

`g(n) = ((9)/(10))^{n-1`

Represent the combination of f(n) and g(n) with A(n)

So, we have:

`A(n) = f(n) * g(n)`

This gives:

`A(n) = 500 * ((9)/(10))^{n-1`

To calculate the 11th term, we make use of n = 11

`A(11) = 500 * ((9)/(10))^{11-1`

`A(11) = 500 * ((9)/(10))^{10`

This gives:

`A(11) = 500 * (0.9)^(10)`

`A(11) = 500 * 0.3486784401`

`A(11) = 174.33922005`

Approximate to 2 dp

`A(11) = 174.34`