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

14 Σ [(1.3^n) * (150)]n = 0
Using the sigma notation to find the sum of his first 15 payments, each of the possible values of n (from 0 to 14) are substituted into the equation. After which, each of the results are then added to each other. Also, the problem states that only the first 15 payments are to be included in the notation. This shows that the series is limited and is finite. Therefore, it is a convergent series.