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 the amount he paid the month before. explain to larry how to represent his first 15 payments in sequence notation. then explain how to find the sum of his first 15 payments, using complete sentences.

Since Larry wants to pay 1.3 times every time he pays, therefore this represents a sequence in the form of geometric series. The general form of geometric series is:

an = a1 (r)^(n - 1)

where,

an = is the value after n months

a1 = initial amount paid or 1st payment = $150

r = is the common ratio = 1.3

n = the total number of months

Substituting the given values,  the equation becomes:

an = 150 (1.3)^(n – 1)

Therefore the first 15 payments in sequence notation is described as:

 ---1st image---

The sum of his first payments (S) would simply be equivalent to:

--- 2nd image---

Therefore this means that Larry can compute for the total 15 payments by plugging in each by each the value of n from 1 to 15 then sum it all up.

Another way would be to use the simplified sequence notation:

S = a1 [(1 – r^n) / (1 – r)]

S = 150 [(1 – 1.3^15) / (1 – 1.3)]

S = $25,092.95