BREAKING: Target Test Prep releases Brand New 2026 On Demand GMAT prep course

Redeem

Sum of arithmetic progression

Problem Solving — algebra and arithmetic (GMAT Focus Edition)
This topic has expert replies
Post new topic Post Reply
Previous Topic Next Topic
Source: — Quantitative Reasoning |
User avatar
Senior | Next Rank: 100 Posts
Posts: 62
Joined: Fri Oct 23, 2009 12:54 pm
Location: Pittsburgh,PA
Thanked: 4 times
Followed by:1 members

by RyanDark » Thu Aug 12, 2010 7:33 am
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
Top
Senior | Next Rank: 100 Posts
Posts: 38
Joined: Wed Aug 11, 2010 8:47 pm
Thanked: 3 times

by Prashantbhardwaj » Thu Aug 12, 2010 11:34 am
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).
Top
Post new topic Post Reply
• Page 1 of 1