Question

Finding the common ratio

Answer 1

Common ration r = 1.5

`F = 300 (1.5)^t\\`

If she pays her ticket on time then it would be 300/1.5 = €200 which is the original ticket fine

Explanation:

The common ration for a geometric progression is given by dividing each term by the previous term

So

r = 450/300 = 675/450 = 1012.50/450 = 1.5

The nth term is given by

`a_n = a_1 \cdot r^n`

where

`\sf{a_1 = first \;term}\\r = common \;ratio\\a_n = nth\;term}`

In this particular case, instead of using
`a_n` we are using F and instead of n we are using t which is the number of months after getting the ticket

So
with first term= 300, r = 1.5 we get

`F = 300(1.5)^t`

This is the fine to be paid after t months delay

Since the fine after 1 month is 300, if she pays her ticket on time then it would be 300/1.5 = €200