Question

Help please!!
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

Doesn't give me any answers to chose from

Answer 2

Ok, the sigma notation, I think, would look something like this
\[Amount Payed= \sum_{t}^{15} 150 * 1.3^{t-1}\]
This is because the first month, Larry pays 150, then every month after that he pays 1.3 time what he paid the previous month. The sigma means that add each month's payment Butterulatively up to 15 months

Answer 3

thank you

Answer 4

By way of explanation, you could think of the first month's payment as being equal to
150 * 1.3^(1-1) or 150 * 1.3 ^ 0 = 150 *1, or just 150.
The second month's payment would be 150 * 1.3^1
Then 150 * 1.3^2 for the third month
Then 150 * 1.3^3 for the fourth month
...
All the way up to 150 * 1.3^14 for the 15th month
These monthly payments get added together to calculate Larry's total payment amount over 15 months

Answer 5

Finally, since the series keeps on increasing to larger and larger amounts without approaching any single point, it would be "divergent"

And it's not a problem, btw; happy to offer support :)

Answer 6

Thank you so much!