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Senior Manager  Joined: 02 Dec 2007
Posts: 349
A certain computer program generates a sequence of numbers a1, a2, … ,  [#permalink]

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Difficulty:   15% (low)

Question Stats: 82% (02:22) correct 18% (02:36) wrong based on 345 sessions

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A certain computer program generates a sequence of numbers a1, a2, … , an such that $$a_1 = a_2 = 1$$ and $$a_k = a_{k-1} + 2a_{k-2}$$ 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 24 Sep 2018, 00:19, edited 2 times in total.
Edited the question.
Manager  Joined: 26 May 2005
Posts: 160
Re: A certain computer program generates a sequence of numbers a1, a2, … ,  [#permalink]

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15
1
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
General Discussion
VP  Joined: 07 Nov 2007
Posts: 1346
Location: New York
Re: A certain computer program generates a sequence of numbers a1, a2, … ,  [#permalink]

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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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Manager  Joined: 18 Jun 2007
Posts: 215
Re: A certain computer program generates a sequence of numbers a1, a2, … ,  [#permalink]

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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: 22
Re: A certain computer program generates a sequence of numbers a1, a2, … ,  [#permalink]

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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: 183
Re: A certain computer program generates a sequence of numbers a1, a2, … ,  [#permalink]

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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: 20 Dec 2010
Posts: 167
Schools: UNC Duke Kellogg
Re: A certain computer program generates a sequence of numbers a1, a2, … ,  [#permalink]

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43...choice B

a5=11; a6=21; a7=43
Director  Joined: 01 Feb 2011
Posts: 551
Re: A certain computer program generates a sequence of numbers a1, a2, … ,  [#permalink]

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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: 551
Re: A certain computer program generates a sequence of numbers a1, a2, … ,  [#permalink]

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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
SVP  Joined: 06 Sep 2013
Posts: 1573
Concentration: Finance
Re: A certain computer program generates a sequence of numbers a1, a2, … ,  [#permalink]

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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 V
Joined: 16 Oct 2010
Posts: 9699
Location: Pune, India
Re: A certain computer program generates a sequence of numbers a1, a2, … ,  [#permalink]

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2
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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Karishma
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Intern  Joined: 20 May 2014
Posts: 31
Re: A certain computer program generates a sequence of numbers a1, a2, … ,  [#permalink]

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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 V
Joined: 16 Oct 2010
Posts: 9699
Location: Pune, India
Re: A certain computer program generates a sequence of numbers a1, a2, … ,  [#permalink]

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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)
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Karishma
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Intern  Joined: 26 Mar 2013
Posts: 15
Location: India
Concentration: Finance, Strategy
Schools: Booth PT '18 (S)
Re: A certain computer program generates a sequence of numbers a1, a2, … ,  [#permalink]

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calculating in sequence

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

Ans B
Manager  Joined: 03 Jan 2015
Posts: 59
Concentration: Strategy, Marketing
WE: Research (Pharmaceuticals and Biotech)
Re: A certain computer program generates a sequence of numbers a1, a2, … ,  [#permalink]

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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
Non-Human User Joined: 09 Sep 2013
Posts: 13144
Re: A certain computer program generates a sequence of numbers a1, a2, … ,  [#permalink]

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