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General arithmetic query

I'm confused but not sure how to explain it, the geometric series goes
S=a+ar+ar^2 etc, but how does it work for the arithmetic series? S=a+(n-1)d...?
Reply 1
Avatar for Russcollins
Russcollins
The sum of an arithmetic series is given by:
S=a+(a+d)+(a+2d)+...+(a+(n-1)d) or
S=na+n(n-1)d/2 or
S=n(a+(n-1)d/2)

This comes from the sum of 1 to n being given by n(n+1)/2 and this is the formula to find the nth triangle number.

Hope this helps.
Reply 2
Avatar for Kippsy
Kippsy
OP
4
Original post by Russcollins
The sum of an arithmetic series is given by:
S=a+(a+d)+(a+2d)+...+(a+(n-1)d) or
S=na+n(n-1)d/2 or
S=n(a+(n-1)d/2)

This comes from the sum of 1 to n being given by n(n+1)/2 and this is the formula to find the nth triangle number.

Hope this helps.


Yeah this is exactly what I was looking for, thanks a lot.

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