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# A sequence of numbers is defined by the formula an = 2^n

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Senior Manager
Joined: 21 Oct 2013
Posts: 444
A sequence of numbers is defined by the formula an = 2^n [#permalink]

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20 Jul 2014, 01:57
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73% (01:09) correct 27% (00:53) wrong based on 152 sessions

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A sequence of numbers is defined by the formula $$a_n = 2^n$$, for any positive integer n. What is the difference between the mth term and the (m−1)th term, in terms of m?

A. 2
B. 2m
C. m^2
D. 2^m
E. 2^(m−1)
[Reveal] Spoiler: OA

Last edited by Bunuel on 20 Jul 2014, 03:49, edited 1 time in total.
Edited the question
Math Expert
Joined: 02 Sep 2009
Posts: 43862
Re: A sequence of numbers is defined by the formula an = 2^n [#permalink]

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20 Jul 2014, 03:52
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goodyear2013 wrote:
A sequence of numbers is defined by the formula $$a_n = 2^n$$, for any positive integer n. What is the difference between the mth term and the (m−1)th term, in terms of m?

A. 2
B. 2m
C. m^2
D. 2^m
E. 2^(m−1)

$$a_m-a_{m-1}=2^m-2^{m-1}=2^m(1-2^{-1})=2^m*\frac{1}{2}=2^{m-1}$$.

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Joined: 23 Jan 2013
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Schools: Cambridge'16
Re: A sequence of numbers is defined by the formula an = 2^n [#permalink]

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24 Oct 2014, 10:45
pick m=3

a3=2^3
a2=2^2

a3-a2=2^3-2^2=2^2 (2-1)=2^2, it is 2^(m-1)

E
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Re: A sequence of numbers is defined by the formula an = 2^n [#permalink]

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29 Sep 2016, 08:42
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Senior Manager
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Re: A sequence of numbers is defined by the formula an = 2^n [#permalink]

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27 Feb 2017, 03:45
Mth term = 2^m
(m-1)th term = 2^(m-1)
Difference = 2^m - 2^(m-1) = 2^(m-1){2-1} = 2^(m-1). Option E
Re: A sequence of numbers is defined by the formula an = 2^n   [#permalink] 27 Feb 2017, 03:45
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