Can you help me with constructing a formula?

A

Arcynical

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Jun 15, 2019
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Hello,

I want to construct a formula to graph an evolution in amount in total payed for x months.
the base cost is 4 and every month the amount paid increases by 2. so in month 1 you pay 4, month 2 you pay 6 and in month 3 you pay 8 etc.
I want to find out what the total amount payed is for x months. so for example in month 3 you would have paid 4+6+8=18
Does anyone want to help me with this?
 
Hello, and welcome to FMH! :)

I would write:

[MATH]S=\sum_{k=2}^{n+1}(2k)=2\left(\sum_{k=1}^{n}(k+1)\right)=n(n+1)+2n=n^2+3n=n(n+3)[/MATH]
 
This is called an Arithmetic progression and is very common in maths. It occurs when you keep adding the same amount (d) to the previous term (A).
The total number of terms bring n

The formula to sum all the terms is simple
An = A1 +(n-1)*d and you should try and remember it.

So in your case A1 (first term) = 4, d (common difference) = 2 and n = x and total amount payed is An
 
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