# Maths C1 sequences and series question

An investor puts £4000 in an account. Every month thereafter she deposits another £200. How much money in total will she have invested at the start of a) the 10th month and b) the mth moth. (note that at the start of the 6th month she will have only made 5 deposits)

--- I am stuck on the first question. I eventually got the answer right by doing £4000 + (9 x 200) = £5,800. But I keep on getting the answer wrong when i use the Sn = n/2[2a + (n-1)d] formula. And I don't understand why.
Original post by crazychitchat
Sn = n/2[2a + (n-1)d] formula. And I don't understand why.

Is it not just 1 a? I can't check as I've not got the formula book handy
Original post by Abby_W31
Is it not just 1 a? I can't check as I've not got the formula book handy

It is 2a.
Original post by SamKeene
It is 2a.

My apologies, it is a year since I've done C1!
Original post by crazychitchat
An investor puts £4000 in an account. Every month thereafter she deposits another £200. How much money in total will she have invested at the start of a) the 10th month and b) the mth moth. (note that at the start of the 6th month she will have only made 5 deposits)

--- I am stuck on the first question. I eventually got the answer right by doing £4000 + (9 x 200) = £5,800. But I keep on getting the answer wrong when i use the Sn = n/2[2a + (n-1)d] formula. And I don't understand why.

You need the tenth term

The sum of the ten terms would give you her total in month 1 plus her total in month 2 plus her total in month 3 etc
Original post by TenOfThem
You need the tenth term

The sum of the ten terms would give you her total in month 1 plus her total in month 2 plus her total in month 3 etc

Ok, I think I understand, but how am I suppose to know whether I am suppose to use the formula or not
Original post by crazychitchat
Ok, I think I understand, but how am I suppose to know whether I am suppose to use the formula or not

I would advise writing down some terms and then reading the question

Here
Month 1 there is 4000
Month 2 there is 4200
Month 3 there is 4400

Etc

So the amount each month is a term in the sequence

The formula you tried to use is for the sum when adding the terms together
If you were told that she invested an extra 200 as well as the previous month's investment, you could use the formula for Sn, as it would form an arithmetic series:

Month 1: 4000
Month 2: 4200
Month 3: 4400
etc.

However, you are told that she only deposits 200 every month, so the progression would look like this:

Month 1: 4000
Month 2: 200
Month 3: 200
etc.

It is actually the total amount in the account that is forming the arithmetic series here, as month 1 is 4000 total, month 2 is 4200 total, and so on. Therefore, each month's total is a term in the series, not the sum of the series, so the formula for Un would be used, not the formula for Sn​.
Original post by lukejoshjames
If you were told that she invested an extra 200 as well as the previous month's investment, you could use the formula for Sn, as it would form an arithmetic series:

Month 1: 4000
Month 2: 4200
Month 3: 4400
etc.

However, you are told that she only deposits 200 every month, so the progression would look like this:

Month 1: 4000
Month 2: 200
Month 3: 200
etc.

It is actually the total amount in the account that is forming the arithmetic series here, as month 1 is 4000 total, month 2 is 4200 total, and so on. Therefore, each month's total is a term in the series, not the sum of the series, so the formula for Un would be used, not the formula for Sn​.

Thank you so much. I understand it.
This is the correct answer they wanted you to use the nth term formula which is a+(n-1)d not the sum in the question they did not ask you about the sum
Original post by Yomna :))
This is the correct answer they wanted you to use the nth term formula which is a+(n-1)d not the sum in the question they did not ask you about the sum

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