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sudhir3127: Legendary Member; Posts: 829; Joined: Mon Jul 07, 2008 10:09 pmFollowed by: 3 members; Location: INDIA; Thanked: 84 times

by sudhir3127 » Thu Aug 07, 2008 8:57 am

Find the value of

1-2-3 + 2-3-4+.........+ 100 terms

Answer after some discussion...

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Source: Beat The GMAT — Problem Solving | Thu Aug 07, 2008 8:57 am

pepeprepa: Legendary Member; Posts: 661; Joined: Tue Jul 08, 2008 12:58 pm; Location: France; Thanked: 48 times

by pepeprepa » Thu Aug 07, 2008 9:01 am

I do not see how the set finishes...
is the end 98-99-100
or 98-99-100+100
or there are 100 terms in the set ?

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sudhir3127: Legendary Member; Posts: 829; Joined: Mon Jul 07, 2008 10:09 pmFollowed by: 3 members; Location: INDIA; Thanked: 84 times

by sudhir3127 » Thu Aug 07, 2008 9:03 am

it says upto 100 terms....

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nitingupta5: Junior | Next Rank: 30 Posts; Posts: 21; Joined: Fri Jul 11, 2008 8:40 am; Thanked: 2 times

by nitingupta5 » Thu Aug 07, 2008 9:06 am

Is it -626

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pepeprepa: Legendary Member; Posts: 661; Joined: Tue Jul 08, 2008 12:58 pm; Location: France; Thanked: 48 times

by pepeprepa » Thu Aug 07, 2008 9:13 am

Yeah I agree with -626
The set goes from
1-2-3
to
33-34-35
34

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sudhir3127: Legendary Member; Posts: 829; Joined: Mon Jul 07, 2008 10:09 pmFollowed by: 3 members; Location: INDIA; Thanked: 84 times

by sudhir3127 » Thu Aug 07, 2008 9:20 am

thanks for the answer...

its -626...

here goes the answer..

1-2-3 + 2-3-4+............+upto 100 terms

-4 + -5 ................33 terms + 34

n= 33

n/2 ( 2a + (n-1 ) d) + 34

33/2 ( 2(-4) + 32(-1) + 34

-660 + 34 = -626

thought it to be a bit tricky.. hence shared...

thanks a lot all..

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pepeprepa: Legendary Member; Posts: 661; Joined: Tue Jul 08, 2008 12:58 pm; Location: France; Thanked: 48 times

by pepeprepa » Thu Aug 07, 2008 9:29 am

Indeed, I do not understand which technique you use?

I used the sum formula:
1-2-3
2-3-4
...
33-34-35
34

T=( "The sum from i=1 to 33" of (i-(i+1)-(i+2)) ) + 34
T=("The sum from i=1 to 33" of (-i-3) ) + 34
T=( 33*(-3) - "The sum from i=1 to 33" of i ) +34
T= (-99 - 33*34/2) + 34
T= -660 + 34

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nitingupta5: Junior | Next Rank: 30 Posts; Posts: 21; Joined: Fri Jul 11, 2008 8:40 am; Thanked: 2 times

by nitingupta5 » Thu Aug 07, 2008 9:36 am

What Sudhir did is added up the first three terms and came up with -4
and the same with the rest

-4, -5,...

It's a faster way to do it

I did the same way as you describe

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