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problem with exponents

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problem with exponents

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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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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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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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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