Question

The table below shows the amount of money, in cents, Celine had in her savings account after different number of years:

Years 2 5 1 4 6 3
Money in cents 36 972 12 324 2,916 108


What will be the amount of money, in cents, that Celine will save in 12 years?
34,992

708,588

2,125,764

2,679,875

Answer 1

The table below shows the amount of money Celine has after each year in ascending order

The amount of money that Celine own has tripled each year, so we know the ratio is 3

Think of this as a sequence;

Term 1 = 12
Term 2 = 36
Term 3 = 108
Term 4 = 324

The sequence has a common ratio, so this sequence is a Geometric Sequence

A geometric sequence general formula is given as

`n_(th) term = ar^(n-1)`

Where
a = the first term = 12
n = the number of term
r = the ratio = 3

Substituting these values into the general form


`n_(th) term =(12)(3)^(n-1)`

Now, we have the formula, we can work out the amount Celine will have when n = 12


`12_(th) term=(12)(3)^(12-11)`

`12_(th) term = (12)(3)^(11) = 2125764`

The answer is 2,125,764