Sum of arithmetic progression

[Jinglander]

Can someone give me a good way to remember the formula, perhaps by explaining the derivation, but anything that works is great

[RyanDark]

Sum of n = (n/2)(a1+an) ----------(1)first term+ nth term
= (n/2)(a1+a1+(n-1)d) -------------(2)putting nth term,an=a1+(n-1)d
S= (n/2)(2a1+(n-1)d))---------------(3)
Where
a1=first term,
an=Nth term

[Prashantbhardwaj]

Basically the formula for summing up the terms in an AP is:

S= (2a+(n-1)d)n/2

where
a is the first term of the series and
n is the total no. of terms and
d is the common difference.

it can also be written as:

S= (a+(a+(n-1)d))n/2

where
a is the first term of the series
n is the total no of terms in the series
d is the common difference
a+(n-1)d is the last term of the series.

The third way to write this formula is

S= n * (a+l)/2.

where a,n are same as above and
l is the last term of the serieswhich is = a+(n-1)d
(a+l)/2 is the arithmetic mean of the whole series and
n is the total no. of terms present in the series.

It might be easier to learn the last formula and derive the basic form from it. But it will cost you some time.
Oh! and i would like to point out that i have used "l" to represent "an" (Nth term).