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

we can use sigma notation

Answer 2

how would that be possible to create

Answer 3

ok first lets do out a few terms , and see if we can find a pattern

Answer 4

I have no clue at all on this topic.
I sorta understood the lesson

Answer 5

so the rule is we multiply last month's payment by 1.3 , starting with 150 as the initial payment.
150 , 150 * 1.3 , (150 * 1.3 ) 1.3 , ...

Answer 6

do you agree so far ?

Answer 7

ofcourse.

Answer 8

we can rewrite this list more easily
instead of multiplying last month by 1.3 , which gets tedious
150 , 150 * 1.3 , (150 * 1.3 ) 1.3 , ((150 *1.3) *1.3) 1.3, ...

we can make a better list
150 , 150 * 1.3 , 150 * 1.3^2 , 150 * 1.3^3

in general we have
150 * 1.3 ^ n , where n = 0,1,2,3,..

Answer 9

okay