Sequences

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sparkle6: Senior | Next Rank: 100 Posts; Posts: 54; Joined: Tue Sep 20, 2011 7:58 amFollowed by: 1 member; Thanked: 1 times

by sparkle6 » Wed Sep 21, 2011 7:51 am

For any positive integer n, the sum of the first n positive integers equals: [n(n+1)]/2. What is the sum of all the even integers between 99 and 301?

A. 10,100
B. 20,200
C. 22,650
D. 40,200
E. 45,150

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Source: Beat The GMAT — Problem Solving | Wed Sep 21, 2011 7:51 am

GMATGuruNY: GMAT Instructor; Posts: 15539; Joined: Tue May 25, 2010 12:04 pmFollowed by: 1906 members; Location: New York, NY; Thanked: 13060 times; GMAT Score:790

by GMATGuruNY » Wed Sep 21, 2011 7:56 am

I posted a solution here:

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gmatclubmember: Master | Next Rank: 500 Posts; Posts: 158; Joined: Sat Sep 03, 2011 10:31 amFollowed by: 2 members; Thanked: 29 times

by gmatclubmember » Wed Sep 21, 2011 7:57 am

The no. of terms would be 101 [(300-100)/2]+1
Sum of n terms = 101/2[200+100*2]=20200.

B is the answer.

Cheers
Ami/-

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cavaliar: Junior | Next Rank: 30 Posts; Posts: 13; Joined: Wed Oct 07, 2009 4:29 am

by cavaliar » Wed Sep 21, 2011 8:04 am

Answer B

Sequence between 2*50 and 2*150 even numbers

so 2*( [(150*151)/2]- [(50*51)/2] + 100

=20200

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Anurag@Gurome: GMAT Instructor; Posts: 3835; Joined: Fri Apr 02, 2010 10:00 pmFollowed by: 523 members; Location: Milpitas, CA; Thanked: 1854 times; GMAT Score:770

by Anurag@Gurome » Wed Sep 21, 2011 7:17 pm

sparkle6 wrote:For any positive integer n, the sum of the first n positive integers equals: [n(n+1)]/2. What is the sum of all the even integers between 99 and 301?

A. 10,100
B. 20,200
C. 22,650
D. 40,200
E. 45,150

We need the sum 100 + 102 + 104 +.....+300 = 100 + (100 + 2) + (100 + 4)....(100 + 200)
= 100*101 + 2*(1 + 2 +..+100) = 100*101 + 2*100*101/2 = 2*100*101 = 20,200

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