Question

A person a pair of shoes is purchased each year and has noticed that the price has increased as a geometric progression. If the price increase in the last two years was 25 dollars and in the last year was 15 dollars.

a. What was the price of the pair of shoes two years ago.
b. A soon as they are sold today.

Answer 1

a ar ar^2

ar^2 - a = 25 or a (r^2-1) = 25

ar^2 - ar = 15 or ar(r-1) = 15

[25/(r^2-1) ] r (r-1) = 15

r (r-1) /[ (r+1)(r-1) ] = 15/25 = 3/5

r/(r+1) = 3/5

5 r = 3 r + 3

2 r = 3
r = 3/2 = 1.5
then a r^2 - a = 25
1.25 a = 25
a = 20
so
20, 30, 45, .....