Question

Larry has taken out a loan for college. He started paying off the loan with a first payment of $150. Each month he pays, he wants to pay back 1.3 times as the amount he paid the month before. Explain to Larry how to represent his first 15 payments in sigma notation. Then explain how to find the sum of his first 15 payments, using complete sentences. Explain why this series is convergent or divergent.

Answer 1

Divergent

Explanation:

We can make use of the exponent function to solve this question. The function would be like:

`an = a_1 (r) ^ {n - 1}`

where
`a_1` is the first payment ,

`r` = ratio of increase ; and

`n` = the number of payments.

So it can be written as:

`f ( n ) = 150 * 1.3 ^ {( n - 1 )}`

The series will keep increasing since the ratio of the function is 1.3 which was > 1 so. Therefore, the series is divergent.