+120 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.
+23247 Starting with $200 and paying 1.2 times as much back each of the following months for a total of 30 months:
200 + 200(1.2) + [200(1.2)](1.2) + [200(1.2)(1.2)](1.2) ... (for 30 terms)
= 200 + 200(1.2) + 200(1.2)2 + 200(1.2)3 + ... + 200(1.2)29
= sigma( 200(1.2)n ) from n = 0 to n = 29.
Since the multiplier (1.2) is greater than 1, this series (if considered to be an infinite series) diverges.
