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

The question can be answered using the exponent function. The function would look like:
an = a1 (r)^(n - 1)
where
a1= initial payment
r= ratio of increase
n= number of payment.

The sigma notation to determine the sum of
  15  Σ  =  150*1.3^(n-1)n = 1
Since the function ratio is 1.3 which was >1, the series will keep increasing so it would be divergent