Question

Claire has $300 in an account. She decides she is going to take half of what's left in there at the end of each month. From the given information. Write the recursive and explicit functions for each geometric sequence. Please use these terms recursive: f(1) = first term, f(n) = pattern*f(n-1). 300 is the starting term and 1/2 is the pattern. explicit is y = pattern^x * 0 term.

Answer 1

The recursive formula is always expressed in terms of a previous term. In the given scenario,

first term, f(1) = 300

This amount reduces by 1/2 each month. Thus, common ratio is 1/2

f(n - 1) refers to the term before n at every given time. Recall, n = number of months. Thus, the recursive formula is

f(n) = 1/2f(n - 1)

Where f(n - 1) is the previous term

The formula for the explicit formula is

an = a1 * r^(n - 1)

Thus,

an = 300 * 1/2^(n - 1)