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?

Answer 1

'more money' is vague. but i spose we could work a general idea from it

Answer 2

nothing is mentioned about interest so i assume this is under his mattress?

Answer 3

its most likely an arithmetic progression summed up over 41 months

Answer 4

I understand arithmetics, but I don't get this specific question. I don't think that interest is part of the question.

Answer 5

i dont spose you recall the formula for the sum of an arithmetic sequence?

Answer 6

Yeah. One sec.

Answer 7

There are two. One is Sn=(n/2)(a_1 + a_n). That one is simpler.

Answer 8

The other one is Sn=(n/2)[2a_1 + (n-1)d].

Answer 9

good, all you need now is to determine what a_41 would be ...

a_n = a_1 + d(n-1) which when subbed in gives the 2nd one you posted

Sn=(n/2)(a_1 + a_n)

Sn=(n/2)(a_1 + (a_1 + d(n-1)))

Sn=(n/2)(a_1 + a_1 + d(n-1))

Sn=(n/2)( 2a_1 + d(n-1))

Answer 10

we know a_1 and n; and S_41 ... so solve for d

Answer 11

But, it says that he added "more money than the month before." Does this mean that there is exponential growth?

Answer 12

let call Sn, K to avoid confusing n parts ...

K = (n/2) (2 a1 + d(n-1))

2K/n = 2 a1 + d(n-1)

2K/n - 2 a1 = d(n-1)

2[ K/n - a1] = d(n-1)

2[ K/n - a1]/(n-1) = d

Answer 13

exponential is a possibility but that was why i said it was vague to start with.

Answer 14

Let's leave that out if we can because it did not tell me to do that.

Answer 15

:)

Answer 16

2[ K/n - a1]/(n-1) = d?
So, what goes in there?
Let me re-check my lesson to see if there is a simpler way real quick.

Answer 17

lol, n=41 is given, a1 =9 is given ... and K is used to avoid overuse of n and is just the end amount he saved up

Answer 18

..which is given

Answer 19

So, 2[ 9,389/n - 9]/(41-1) = d?

Answer 20

yes, but you missed an 'n' :)

Answer 21

2[ 9,389/41 - 9]/(41-1)

2[ 9,389/41 - 9]/(40)

(9,389/41 - 9)/20

etc ...

Answer 22

Why did the 40 go to a 20?

Answer 23

2/40 = 1/20 of course :/

Answer 24

I thought that it was being multiplied by 2.

Answer 25

write it down on paper if you have to ...
\[\large \frac{2(\frac{9389}{41}-9)}{41-1}\]
\[\large \frac{\cancel2^1(\frac{9389}{41}-9)}{\cancel{40}_{20}}\]

Answer 26

My options are:
$11.00
$11.50
$12.00
$12.50

Answer 27

yeah, we get one of those ...

Answer 28

I got about 14...?

Answer 29

might need new batteries in your calculator then

https://www.google.com/search?q=9%2C389%2F41+-+9)%2F20&oq=9%2C389%2F41+-+9)%2F20&aqs=chrome..69i57j0.816j0j8&sourceid=chrome&espv=210&es_sm=93&ie=UTF-8

Answer 30

Oh, no. It was my own stupid fault. I put the data in wrong. My bad.

Answer 31

:) good luck and all. i gotta meet a guy about a thing

Answer 32

Thanks for your help. Have a good one.