i came up with and proved this shortcut myself :D

its for finding the difference in an arithmetic series when two non-consecutive values. i.e., A sub 3 and A sub 56

given: difference (d) = A sub(n+1) - A sub(n)
n > 0
c > 0
assume all () mean sub from now on
______________________________________________________
prove:
A(n+c)-A(n)
__________ = d
(n+c)-(n)
______________________________________________________
so
A(n+c) - A(n) = (c)(d)

and

(n+c) - (n)
(n) + (c) + (-n) = (c)

therefore

A(n+c) - A(n) (c)(d)
___________ = _____ = d
(n+c) - (n) (c)


:D think this was awesome? donate to me for no reason! think i'm stupid? please tell me so in great detail! :D

 

xD