Question

Mike started a savings account by depositing $9. Each month, he deposits more money than the month before. At the end of 41 months, he has saved $9,389.00. How much more does he deposit each month?

$11.00

$11.50

$12.00

$12.50

Answer 1

Let the extra amount he deposits be x.
You can consider this as an arithmetic progression where 9 is the first term and x is the common difference between successive terms.
So the total amount($9389) would be equal to :
9 + (9+x) + (9+x+x) ......
= 9 + (9+x) + (9+2x) ....
He deposits these amounts for 41 months so there are 41 terms in that sequence.
So now you can form an equation:
\[\frac{ 41 }{ 2 }([2 \times 9] + (41-1)x) = 9389\]

Answer 2

You can solve that equation to find x.
The left hand side of that equation comes from the formula for the sum of n terms of an arithmetic progression:
\[S _{n} = \frac{ n }{ 2 }(2a + (n-1)d)\]

Answer 3

@Prathamesh_M sorry it took me so long to reply, thank you!

Answer 4

Welcome!