Question

Your eccentric Aunt Isabella sends money to each niece and nephew on his or

her birthday, She gives each child $10 on his or her first birthday. On each


birthday thereafter, you and your cousins get $20 more than on the birthday


before. How old will you be when you have received a total of $4,000 from


Aunt Isabella?


How old will you be when you have Received a total Of $4000 from aunt Isabell?

Answer 1

20 years old

Explanation:

Given

Base Amount = $10

Additional Amount = $20

Required

Determine the number of years where the total will accumulate to $4000

This question represents Sum of an AP series.

`S_n = (n)/(2)(2a + (n - 1)d)`

Such that:

`S_n = 4000`

`a = 10`

`d = 20`

Substitute these values in the above formula:

`4000 = (n)/(2)(2 * 10 + (n - 1) * 20)`

`4000 = (n)/(2)(20 + 20n - 20)`

`4000 = (n)/(2)(20n)`

`4000 = (20n^2)/(2)`

`4000 = 10n^2`

Divide through by 10

`400 = n^2`

Take square root of both sides

`20 = n`

`n = 20`