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

very difficult please help!

Answer 2

@anitasonia98
@kirbykirby

Answer 3

last one i promise

Answer 4

I have no idea what sigma notation is xP

Answer 5

:(

Answer 6

I'm sowwy >.<

Answer 7

thanks anyway

Answer 8

@kirbykirby i know youre gonna be a lifesaver lol

Answer 9

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
\[=150+150(1.3)+150(1.3)(1.3) + \ldots+150(1.3)^{14}\\
=\sum_{n=0}^{14}150(1.3)^n=150\sum_{n=0}^{14}(1.3)^n\]

Answer 10

perfect explanation.. thank you!

Answer 11

:)

Answer 12

was this convergent or divergent

Answer 13

@sochittasal convergent since you have a finite sum.