Question

John has taken out a loan for college. He started paying off the loan with a first payment of $100. Each month he pays, he wants to pay back 1.1 times as the amount he paid the month before. Explain to John how to represent his first 20 payments in sigma notation. Then explain how to find the sum of his first 20 payments, using complete sentences. Explain why this series is convergent or divergent.

Answer 1

@thekefentse

Answer 2

I've gotten this far in my answer:

John will represent his first 20 payments in sigma notation as follows:

first payment(1.1 times the amount he paid the previous month)^month number

In sigma notation it will be
20Σn=1 100(1.1)^n

To find the sum, he will have to put it in a series, replacing n with the consecutive numbers 1-19 (20th payment already accounted for in the first)

100 + 100*1.1 + 100*1.1^2 + 100*1.1^3 + ... + 100*1.1^19
100(1 + 1.1 + 1.1^2 + 1.1^3 + ... + 1.1^19)

Answer 3

\[\sum_{n=1}^{20}= 100*(1.10)n\]or\[\sum_{n=1}^{20}= 100*(1.10)^n\]?
how did you get \[1.1^n\]

Answer 4

I'm legitimately asking, sigma wasn't my strongest.

Answer 5

1.1 times the amount he paid the month before

Answer 6

So you're saying use the \[(1.10)^n\] yes?

Answer 7

yup

Answer 8

to find the sum would he have to put it in a series? or just plug in 20

Answer 9

for the sum it would be the series.

Answer 10

if you just plugged in 20 you would get the result for 20, but not 19, 18, 17...

Answer 11

oh okay so let me try

Answer 12

5727.50?