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# If the sequence x{_1} , x{_2} , x{_3} , ...., x{_n} , ....is

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Manager
Joined: 31 Oct 2007
Posts: 113
Location: Frankfurt, Germany
Followers: 1

Kudos [?]: 30 [0], given: 0

If the sequence x{_1} , x{_2} , x{_3} , ...., x{_n} , ....is [#permalink]  17 Jul 2008, 02:03
If the sequence $$x{_1}$$, $$x{_2}$$, $$x{_3}$$, ...., $$x{_n}$$, ....is such that $$x{_1}$$ = 3 and $$x{_n_+_1}$$ = $$2x{_n} - 1$$ for n >= 1, then $$x{_2_0}$$ - $$x{_1_9}$$ =

A. $$2^{19}$$
B. $$2^{20}$$
C. $$2^{21}$$
D. $$2^{20} -1$$
E. $$2^{21} -1$$
_________________

Jimmy Low, Frankfurt, Germany
Blog: http://mytrainmaster.wordpress.com
GMAT Malaysia: http://gmatmalaysia.blogspot.com

Director
Joined: 12 Jul 2008
Posts: 518
Schools: Wharton
Followers: 16

Kudos [?]: 122 [1] , given: 0

Re: Math Set 1: Q25 [#permalink]  17 Jul 2008, 02:51
1
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jimmylow wrote:
If the sequence $$x{_1}$$, $$x{_2}$$, $$x{_3}$$, ...., $$x{_n}$$, ....is such that $$x{_1}$$ = 3 and $$x{_n_+_1}$$ = $$2x{_n} - 1$$ for n >= 1, then $$x{_2_0}$$ - $$x{_1_9}$$ =

A. $$2^{19}$$
B. $$2^{20}$$
C. $$2^{21}$$
D. $$2^{20} -1$$
E. $$2^{21} -1$$

A

if you do out the first few, you'll see a pattern.

x1 = 3
x2 = 2*3-1 = 5
x3 = 2*5-1 = 9
x4 = 2*9-1 = 17

x2-x1 = 2
x3-x2 = 4 = 2^2
x4-x3 = 2^3
.
.
.
x20-x19 = 2^19
Manager
Joined: 31 Oct 2007
Posts: 113
Location: Frankfurt, Germany
Followers: 1

Kudos [?]: 30 [0], given: 0

Re: Math Set 1: Q25 [#permalink]  17 Jul 2008, 03:00
Thks mate. 1 kudos for you
_________________

Jimmy Low, Frankfurt, Germany
Blog: http://mytrainmaster.wordpress.com
GMAT Malaysia: http://gmatmalaysia.blogspot.com

Director
Joined: 14 Aug 2007
Posts: 734
Followers: 8

Kudos [?]: 124 [0], given: 0

Re: Math Set 1: Q25 [#permalink]  17 Jul 2008, 03:46
jimmylow wrote:
If the sequence $$x{_1}$$, $$x{_2}$$, $$x{_3}$$, ...., $$x{_n}$$, ....is such that $$x{_1}$$ = 3 and $$x{_n_+_1}$$ = $$2x{_n} - 1$$ for n >= 1, then $$x{_2_0}$$ - $$x{_1_9}$$ =

A. $$2^{19}$$
B. $$2^{20}$$
C. $$2^{21}$$
D. $$2^{20} -1$$
E. $$2^{21} -1$$

every term in sequence is 2^n + 1....where n >=1

x20 = 2^20 + 1
x19 = 2^19 + 1

subtracting x19 from x20

2*2^19 + 1 - 2^19 -1

2^19(2-1)

2^19

A.
Re: Math Set 1: Q25   [#permalink] 17 Jul 2008, 03:46
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# If the sequence x{_1} , x{_2} , x{_3} , ...., x{_n} , ....is

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