Tom has taken out a loan for college. He started paying off the loan with a first payment of $200. Each month he pays, he wants to pay back 1.2 times as the amount he paid the month before. Explain to Tom how to represent his first 30 payments in sigma notation. Then explain how to find the sum of his first 30 payments, using complete sentences. Explain why this series is convergent or divergent.

This is a geometric series. The first payment represents the first term, a. The number of times he wants to pay back for subsequent payments represent the common ration, r. The first 30 payments represents the number of terms to use in finding the sum, n.

Hence, a = $ 200, n = 30 and r = 1.2.

The sum of a geometric sequence is given as:

Sn = (a ((r^n) - 1)) / (r-1)

= (200 ((1.2^30) - 1)) / (1.2-1)

= $ 236, 376. 31

Explain why this series is convergent or divergent.

Since the common ratio, r, is greater than 1, the series is divergent