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# geometric series

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geometric series [#permalink]  15 Dec 2010, 12:08
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In a sequence 1,2,4,8,16,32......each term after the first is twice the previous term. What is the sum of the 16th, 17th and 18th tems in the sequence ?

a. 2^18
b. 3(2^17)
c. 7(2^16)
d. 3(2^16)
e. 7(2^15)

Could some tell me the basic formula for handling geometric series. Thanks.
[Reveal] Spoiler: OA

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Ajit

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Re: geometric series [#permalink]  15 Dec 2010, 12:30
ajit257 wrote:
In a sequence 1,2,4,8,16,32......each term after the first is twice the previous term. What is the sum of the 16th, 17th and 18th tems in the sequence ?

a. 2^18
b. 3(2^17)
c. 7(2^16)
d. 3(2^16)
e. 7(2^15)

Could some tell me the basic formula for handling geometric series. Thanks.

Given:
a_1=2^0=1;
a_2=2^1=2;
a_3=2^2=4;
...
a_n=2^{n-1};

Thus a_{16}+a_{17}+a_{18}=2^{15}+2^{16}+2^{17}=2^{15}(1+2+4)=7*2^{15}.

So you don't actually need geometric series formula.

Answer: E.

But still if you are interested:

Sum of the first n terms of geometric progression is given by: sum=\frac{b*(r^{n}-1)}{r-1}, where b is the first term, n # of terms and r is a common ratio \neq{1}.

Sum of infinite geometric progression with common ratio |r|<1, is sum=\frac{b}{1-r}, where b is the first term.

Hope it helps.
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Re: geometric series [#permalink]  15 Dec 2010, 21:21
Given:
a_1=2^0=1;
a_2=2^1=2;
a_3=2^2=4;
...
a_n=2^{n-1};

Thus a_{16}+a_{17}+a_{18}=2^{15}+2^{16}+2^{17}=2^{15}(1+2+4)=7*2^{15}.

So you don't actually need geometric series formula.

Thanks very Much! This is an excellent approach.
Manager
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In the sequence 1, 2, 4, 8, 16, 32, …, each term after the f [#permalink]  14 Feb 2011, 17:11
In the sequence 1, 2, 4, 8, 16, 32, …, each term after the first is twice the previous term. What is the sum of the 16th, 17th, and 18th terms in the sequence?

A. 2^18
B. 3(2^17)
C. 7(2^16)
D. 3(2^16)
E. 7(2^15)
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Joined: 02 Sep 2009
Posts: 11517
Followers: 1792

Kudos [?]: 9537 [0], given: 826

Re: In the sequence 1, 2, 4, 8, 16, 32, …, each term after the f [#permalink]  14 Feb 2011, 17:33
Merging similar topics.
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Re: In the sequence 1, 2, 4, 8, 16, 32, …, each term after the f   [#permalink] 14 Feb 2011, 17:33
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# geometric series

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