Question

FAN+MEDAL
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.
is this covergent or divergent

Answer 1

Ok so:
1st payment: 150
2nd payment: 150(1.3) = 195
3rd payment: 150(1.3) * 1.3 = 195 * 1.3 (he wants to pay 1.3 times the last month's payment which was 195, of just 150(1.3)

4th payment: 150(1.3)(1.3)(1.3)
....
15th payment: 150(1.3)14

So,
All paymets = 1st payment + 2nd payment + ... + 15th payment
=150+150(1.3)+150(1.3)(1.3)+…+150(1.3)^\[\sum_{n=0}^{14} 150(1.3)^n = 150 \sum_{n=0}^{14} (1.3)^n\]

Answer 2

This is also convergent since you have a finite sum.