problem with exponents

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zach: Newbie | Next Rank: 10 Posts; Posts: 2; Joined: Fri Jan 18, 2008 6:27 am

by zach » Wed Mar 05, 2008 3:55 am

Hello,
I would really appreciate if somebody could please explain the solution to below GMAT prep question:

2+2+2^2+2^3+2^4+2^5+2^6+2^7+2^8

2^9 (correct answer)

2^10

2^16

2^35

2^37

thanks

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Source: Beat The GMAT — Problem Solving | Wed Mar 05, 2008 3:55 am

camitava: Legendary Member; Posts: 645; Joined: Wed Sep 05, 2007 4:37 amFollowed by: 5 members; Location: India; Thanked: 34 times

by camitava » Wed Mar 05, 2008 4:07 am

zach,
This problem is basically a G.P problem. G.P. means Geometric Progression.
2+2+2^2+2^3+2^4+2^5+2^6+2^7+2^8
= 2 + 2(2^8 - 1)
= 2^9
Got my point, zach? By the way, if u want to know much about GP, u can do a Google-search. Otherwise, the formula for GP is -
Sn = Sum of n terms = a(r^n - 1)/(r - 1) where a = first term = 2 (here)
r = common diff = 2^2/2 = 2 (here) and n = 8.
Look I have kept the first 2 out of the series and started from the second one till end.

Correct me If I am wrong

Regards,

Amitava

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zach: Newbie | Next Rank: 10 Posts; Posts: 2; Joined: Fri Jan 18, 2008 6:27 am

by zach » Wed Mar 05, 2008 4:15 am

hi Amitava,

I get it now, thank you very much for your explanation

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xilef: Master | Next Rank: 500 Posts; Posts: 111; Joined: Thu Jan 31, 2008 4:05 pmFollowed by: 1 member; Thanked: 18 times

by xilef » Wed Mar 05, 2008 2:18 pm

another solution:

2+2 = 4 = 2^2

2+2+2^2 is the same as 2^2+2^2 = 2^3

2^3 + 2^3 = 2^4 and so on... 2^8 + 2^8 = 2^9

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