Sum_progessions

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gmatmachoman: Legendary Member; Posts: 2326; Joined: Mon Jul 28, 2008 3:54 amFollowed by: 2 members; Thanked: 173 times; GMAT Score:710

by gmatmachoman » Fri May 28, 2010 3:04 am

The sum of the fourth and twelfth term of an arithmetic progression is 20. What is the sum of the first 15 terms of
the arithmetic progression?

A. 300
B. 120
C. 150
D. 170
E. 270

R&D on GMAT algorithm:

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Source: Beat The GMAT — Problem Solving | Fri May 28, 2010 3:04 am

gmatjedi: Senior | Next Rank: 100 Posts; Posts: 85; Joined: Sat Aug 15, 2009 4:36 am; Thanked: 19 times

by gmatjedi » Fri May 28, 2010 3:17 am

a(n)=a(1)+(n-1)d

a(4)=a(1)+3d
a(12)=a(1)+11d

a(4)+a(12)=20

20=2a(1)+14d

10=a(1)+7d
therefore a(1)=3 and d=1

start sequence at 3...17

sum of first 15 terms= (3+17)/2 * 15= 150

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liferocks: Legendary Member; Posts: 576; Joined: Sat Mar 13, 2010 8:31 pmFollowed by: 1 member; Thanked: 97 times

by liferocks » Fri May 28, 2010 4:23 am

T(4)=a+3d
T(12)=a+11d
T(4)+T(12)=2a+14d=20

S(15)=15/2*(2a+14d)=15/2 * 20=150

Ans option C

"If you don't know where you are going, any road will get you there."
Lewis Carroll

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selango: Legendary Member; Posts: 1460; Joined: Tue Dec 29, 2009 1:28 amFollowed by: 7 members; Thanked: 135 times

by selango » Fri May 28, 2010 8:15 am

AP formula =n/2[2a+(n-1)d]

nth term = a+(n-1)d

4th term =a+3d

12th term=a+11d

-->a+3d+a+11d=20
2a+14d=20

Substituting in AP formula with n=15

15/2[2a+14d]

15/2*20

=150

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odod: Senior | Next Rank: 100 Posts; Posts: 56; Joined: Tue Jan 13, 2009 12:59 pm; Location: Toronto; Thanked: 1 times

by odod » Fri May 28, 2010 12:55 pm

Hello.

I need some help understanding this solution.

what is a(n)=a(1)+(n-1)d ?. Is that formula to know for the gmat. If so, can someone please explain it to me?

I would appreciate any help.

Thanks

ODOD

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kevincanspain: GMAT Instructor; Posts: 613; Joined: Thu Mar 22, 2007 6:17 amFollowed by: 64 members; Location: madrid; Thanked: 171 times; GMAT Score:790

by kevincanspain » Fri May 28, 2010 1:34 pm

gmatmachoman wrote:The sum of the fourth and twelfth term of an arithmetic progression is 20. What is the sum of the first 15 terms of
the arithmetic progression?

A. 300
B. 120
C. 150
D. 170
E. 270

If the sum of the 4th and 12th term is 20, so is the sum of the 1st and 15th. Thus we have 15 terms that have a mean of 20/2 = 10. Sum= 150

Kevin Armstrong
GMAT Instructor
Gmatclasses
Madrid

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HPengineer: Master | Next Rank: 500 Posts; Posts: 165; Joined: Wed Mar 24, 2010 8:02 amFollowed by: 1 member; Thanked: 2 times

by HPengineer » Fri May 28, 2010 1:42 pm

Here a link to the formula used from wikipedia... Might shed some light

https://en.wikipedia.org/wiki/Arithmetic_progression

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