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Trying to teach myself maths and I realise this is a very basic question (and probably a basic concept), but I don't know how to express what I'm looking for (my Google skills are letting me down...)

If I wanted to repeatedly subtract n from a, I understand that the number of times (t) I'd have to do that to reach zero could be expressed as t = a/n

What I don't understand, is how I can use t to sum the total of the result of each subtraction.

So, if a = 5 and n = 1...

b = 4

c = 3

d = 2

e = 1

f = 0

The sum of b to f is 10.

What I'd like to understand is how I can express the formula to find s when a and n are known.

So s = ???

Realise I've probably not worded this very clearly, so questions are welcome.

Git Gud
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user2781522
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1 Answers1

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You are looking for the sum of an arithmetic progression.

The formula you're looking for is $$ \sum_{k=0}^{t} (c + k n) = (t+1) c + n \binom{t+1}{2} = (t+1) c + n \frac{(t+1)t}{2}. $$ Possibly you are only interested in the special case $c = 0$.

Andreas Caranti
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