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 the amount he paid the month before. Explain to John how to represent his first 20 payments in sequence notation. Then explain how to find the sum of his first 20 payments, using complete sentences.

Answer 1

@Vocaloid

Answer 2

a = the initial term, or in your case, the first payment made (100)
r = the common ratio, or in your case, since he pays 1.1 times the previous month amount, r = 1.1
n = the number of payments, or in your case, 20

plugging these in will give you your sequence notation

Answer 3

actually just a moment

Answer 4

yes i did that i got An=100*1.1^20-1

Answer 5

actually since they want all 20 payments represented I would actually use sigma notation

Answer 6

ohh okay

Answer 7

so yeah, sigma from k = 0 to 20, a = 100, r = 1.1, that will give you your sigma expression

then to find the sum you would just use the formula on the right, plug in the a, r, and n values to get the sum

Answer 8

ok but i technically did not learn about sigma notation

Answer 9

huh

well in that case you could write it out using the first method, so

an = a(r)^(n-1) giving us

an = 100(1.1)^0 , 100(1.1)^1 , 100(1.1)^2... 100(1.1)^(n-1) as a possible way to represent the sequence i gues

Answer 10

would n represent 20?

Answer 11

ah, yes, since you have n = 20 you would have to plug that in to get

a20 = 100(1.1)^0 , 100(1.1)^1 , 100(1.1)^2... 100(1.1)^(20-1)

Answer 12

got 572.24 i feel like thats wrong

Answer 13

no wait i meant to type 572.74

Answer 14

(something was wrong w/ the other formula)

Answer 15

S = a(r^n-1)/(r-1) = 100(1.1^20 - 1)/(1.1-1) = ?

Answer 16

519.68

Answer 17

be careful with PEMDAS

1.1^20
then -1

then divide by (1.1-1)

then multiply the result by 100

Answer 18

i did the first part right but the second part i didn't divide yet so now i got 420.68

Answer 19

1.1^20 = 6.72749994932560009201

subtract 1 to get

5.72749994932560009201

divide by (1.1-1) to get

57.2749994932560009201

multiply by 100 to get

5727.49994932560009201

rounding to the hundredth place

$5727.50 = your sum

Answer 20

When i divide 1.1-1 i get 4.20 though thats whats throwing off my answers

Answer 21

you have to put (1.1-1) in parentheses

5.72749994932560009201/(1.1-1)

Answer 22

OHHHHHH

Answer 23

otherwise it will interpret this as, divide by 1.1 then subtract 1

Answer 24

HAHA im stupid thank you soooo muchhhhhh