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
