Answered

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 :

MrRoyal

Answer:

20 years old

Step-by-step 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.

[tex]S_n = \frac{n}{2}(2a + (n - 1)d)[/tex]

Such that:

[tex]S_n = 4000[/tex]

[tex]a = 10[/tex]

[tex]d = 20[/tex]

Substitute these values in the above formula:

[tex]4000 = \frac{n}{2}(2 * 10 + (n - 1) * 20)[/tex]

[tex]4000 = \frac{n}{2}(20 + 20n - 20)[/tex]

[tex]4000 = \frac{n}{2}(20n)[/tex]

[tex]4000 = \frac{20n^2}{2}[/tex]

[tex]4000 = 10n^2[/tex]

Divide through by 10

[tex]400 = n^2[/tex]

Take square root of both sides

[tex]20 = n[/tex]

[tex]n = 20[/tex]

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