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

Answer:

$A(n) = 500 * (\frac{9}{10})^{n-1$

$A(11) = 174.34$

Step-by-step explanation:

Given

$f(n) = 500$

$g(n) = (\frac{9}{10})^{n-1$

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

So, we have:

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

This gives:

$A(n) = 500 * (\frac{9}{10})^{n-1$

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

$A(11) = 500 * (\frac{9}{10})^{11-1$

$A(11) = 500 * (\frac{9}{10})^{10$

This gives:

$A(11) = 500 * (0.9)^{10}$

$A(11) = 500 * 0.3486784401$

$A(11) = 174.33922005$

Approximate to 2 dp

$A(11) = 174.34$