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# A certain computer program generates a sequence of numbers

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Senior Manager
Joined: 02 Dec 2007
Posts: 428
A certain computer program generates a sequence of numbers [#permalink]

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Updated on: 11 Dec 2013, 01:45
5
00:00

Difficulty:

15% (low)

Question Stats:

80% (01:56) correct 20% (01:40) wrong based on 272 sessions

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A certain computer program generates a sequence of numbers a1, a2, … , an such that a1 = a2 = 1 and ak = ak-1 + 2ak-2 for all integers k such that 3 ≤ k ≤ n. If n > 6, then a7 = ?

A. 32
B. 43
C. 64
D. 100
E. 128

Originally posted by Nihit on 13 Sep 2008, 07:56.
Last edited by Bunuel on 11 Dec 2013, 01:45, edited 1 time in total.
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Joined: 07 Nov 2007
Posts: 1738
Location: New York

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13 Sep 2008, 09:36
2
Nihit wrote:
A certain computer program generates a sequence of numbers a1, a2, … , an such that a1 = a2 = 1 and ak = ak-1 + 2ak-2 for all integers k such that 3 ≤ k ≤ n. If n > 6, then a7 = ?

A. 32
B. 43
C. 64
D. 100
E. 128

a1=1
a2=1
a3=a2+2a1= 3
a4=a3+2a2=5
a5=11
a6=21
a7=43

B
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Senior Manager
Joined: 18 Jun 2007
Posts: 274

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14 Sep 2008, 23:05
another B

just for convenience I will explain lil bit more

Ak= A(k-1) + 2* A(k-2)

in other words every A in this sequence is the sum of pervious term and twice the term that is prev. to prev.....lol it would be easier with working

A1= 1 and A2= 1

A(3)= A(3-1) + A(3-2)
=> = A(2) + 2(A1)
=> = 1 + 2*1
A(3)= 3
And with similar pattern,

A(4)= 3 + 2*1 = 5
A(5)= 5 + 2*3 = 11
A(6)= 11 + 2*5 = 21
A(7)= 21 + 2*11 = 43
Intern
Joined: 28 Jan 2010
Posts: 29

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01 Mar 2010, 07:10
x2suresh wrote:
Nihit wrote:
A certain computer program generates a sequence of numbers a1, a2, … , an such that a1 = a2 = 1 and ak = ak-1 + 2ak-2 for all integers k such that 3 ≤ k ≤ n. If n > 6, then a7 = ?

A. 32
B. 43
C. 64
D. 100
E. 128

a1=1
a2=1
a3=a2+2a1= 3
a4=a3+2a2=5
a5=11
a6=21
a7=43

B

I solved by breaking up a7 until I reached a1 and a2. But it took me while to reach the correct answer.
Manager
Joined: 01 Feb 2010
Posts: 241

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03 Mar 2010, 10:12
Nihit wrote:
A certain computer program generates a sequence of numbers a1, a2, … , an such that a1 = a2 = 1 and ak = ak-1 + 2ak-2 for all integers k such that 3 ≤ k ≤ n. If n > 6, then a7 = ?

A. 32
B. 43
C. 64
D. 100
E. 128

it's B.
a3= a2+a1 = 3
a4 = 3+2 = 5
a5 = 5+6=11
a6=11+10=21
a7=21+22=43

This may be a better way to solve this as there no constant difference between two consecutive terms like in AP.
Manager
Joined: 26 May 2005
Posts: 193

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03 Mar 2010, 11:53
11
Nihit wrote:
A certain computer program generates a sequence of numbers a1, a2, … , an such that a1 = a2 = 1 and ak = ak-1 + 2ak-2 for all integers k such that 3 ≤ k ≤ n. If n > 6, then a7 = ?

A. 32
B. 43
C. 64
D. 100
E. 128

Solving as mentioend earlier always helps but here's another approach for this particular problem
a1 and a2 are odd and a3 would be odd and all the numbers in the sequence are odd as they are of the format
odd number + 2 * odd number.
a7 is odd and only B has an odd number

B
Manager
Joined: 20 Dec 2010
Posts: 215
Schools: UNC Duke Kellogg

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28 Jun 2011, 11:51
43...choice B

a5=11; a6=21; a7=43
Director
Joined: 01 Feb 2011
Posts: 686

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29 Jun 2011, 17:06
a1 = a2 =1
a3 = a2+2a1 = 3
a4 = a3+2a2 = 5
a5 = a4+2a3 = 11
a6 = a5+2a4 = 21
a7 = a6+2a5 = 43

Director
Joined: 01 Feb 2011
Posts: 686

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29 Jun 2011, 17:08
even though this is good observation. this approach wont work if there are more than 1 odd number in the answer choices.

chix475ntu wrote:
Nihit wrote:
A certain computer program generates a sequence of numbers a1, a2, … , an such that a1 = a2 = 1 and ak = ak-1 + 2ak-2 for all integers k such that 3 ≤ k ≤ n. If n > 6, then a7 = ?

A. 32
B. 43
C. 64
D. 100
E. 128

Solving as mentioend earlier always helps but here's another approach for this particular problem
a1 and a2 are odd and a3 would be odd and all the numbers in the sequence are odd as they are of the format
odd number + 2 * odd number.
a7 is odd and only B has an odd number

B
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Joined: 06 Sep 2013
Posts: 1886
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17 Feb 2014, 13:24
x2suresh wrote:
Nihit wrote:
A certain computer program generates a sequence of numbers a1, a2, … , an such that a1 = a2 = 1 and ak = ak-1 + 2ak-2 for all integers k such that 3 ≤ k ≤ n. If n > 6, then a7 = ?

A. 32
B. 43
C. 64
D. 100
E. 128

a1=1
a2=1
a3=a2+2a1= 3
a4=a3+2a2=5
a5=11
a6=21
a7=43

B

Why do they give you this stuff? '3 ≤ k ≤ n. If n > 6'?

Thanks
Cheers
J
Veritas Prep GMAT Instructor
Joined: 16 Oct 2010
Posts: 8097
Location: Pune, India

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17 Feb 2014, 21:29
jlgdr wrote:
x2suresh wrote:
Nihit wrote:
A certain computer program generates a sequence of numbers a1, a2, … , an such that a1 = a2 = 1 and ak = ak-1 + 2ak-2 for all integers k such that 3 ≤ k ≤ n. If n > 6, then a7 = ?

A. 32
B. 43
C. 64
D. 100
E. 128

a1=1
a2=1
a3=a2+2a1= 3
a4=a3+2a2=5
a5=11
a6=21
a7=43

B

Why do they give you this stuff? '3 ≤ k ≤ n. If n > 6'?

Thanks
Cheers
J

Because the relation they gave you $$a_k = a_{k-1} + 2a_{k-2}$$ holds only from the third term onwards till the last term $$a_n$$. That is, k should be 3 or more and will take the last value of n. This relation doesn't hold for the first and second terms and holds for all the rest of the terms. That is what this 'stuff' specifies.

If n > 6 tells you that the sequence has more than 6 terms i.e. at least 7 terms.
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Get started with Veritas Prep GMAT On Demand for $199 Veritas Prep Reviews Intern Joined: 20 May 2014 Posts: 32 Re: A certain computer program generates a sequence of numbers [#permalink] ### Show Tags 03 Jul 2014, 09:58 rishi2377 wrote: another B just for convenience I will explain lil bit more Ak= A(k-1) + 2* A(k-2) in other words every A in this sequence is the sum of pervious term and twice the term that is prev. to prev.....lol it would be easier with working A1= 1 and A2= 1 A(3)= A(3-1) + A(3-2) => = A(2) + 2(A1) => = 1 + 2*1 A(3)= 3 And with similar pattern, A(4)= 3 + 2*1 = 5 A(5)= 5 + 2*3 = 11 A(6)= 11 + 2*5 = 21 A(7)= 21 + 2*11 = 43 why isn't the 2 being multiplied when you do this : A(3)= A(3-1) + A(3-2) isn't the rule given :A(k-1) + 2* A(k-2) Veritas Prep GMAT Instructor Joined: 16 Oct 2010 Posts: 8097 Location: Pune, India Re: A certain computer program generates a sequence of numbers [#permalink] ### Show Tags 03 Jul 2014, 19:13 sagnik2422 wrote: rishi2377 wrote: another B just for convenience I will explain lil bit more Ak= A(k-1) + 2* A(k-2) in other words every A in this sequence is the sum of pervious term and twice the term that is prev. to prev.....lol it would be easier with working A1= 1 and A2= 1 A(3)= A(3-1) + A(3-2) => = A(2) + 2(A1) => = 1 + 2*1 A(3)= 3 And with similar pattern, A(4)= 3 + 2*1 = 5 A(5)= 5 + 2*3 = 11 A(6)= 11 + 2*5 = 21 A(7)= 21 + 2*11 = 43 why isn't the 2 being multiplied when you do this : A(3)= A(3-1) + A(3-2) isn't the rule given :A(k-1) + 2* A(k-2) That's just a typo. Note the next step of the poster: A(3) = A(2) + 2(A1) _________________ Karishma Veritas Prep | GMAT Instructor My Blog Get started with Veritas Prep GMAT On Demand for$199

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Re: A certain computer program generates a sequence of numbers [#permalink]

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19 Jan 2015, 01:20
calculating in sequence

1,1,3,5,11,21,43

Ans B
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Joined: 03 Jan 2015
Posts: 65
Concentration: Strategy, Marketing
WE: Research (Pharmaceuticals and Biotech)
Re: A certain computer program generates a sequence of numbers [#permalink]

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11 Mar 2015, 08:13
Nihit wrote:
A certain computer program generates a sequence of numbers a1, a2, … , an such that a1 = a2 = 1 and ak = ak-1 + 2ak-2 for all integers k such that 3 ≤ k ≤ n. If n > 6, then a7 = ?

A. 32
B. 43
C. 64
D. 100
E. 128

Hi,

It will help if (k-1) and (k-2) are written as subscript. Initially, I understood it to be (ak-1+2ak-2) which, without sub-scripting equals ak + 2ak - 3.

TO
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Re: A certain computer program generates a sequence of numbers [#permalink]

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06 Oct 2017, 21:25
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Re: A certain computer program generates a sequence of numbers   [#permalink] 06 Oct 2017, 21:25
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