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For the sequence a1,a2,a3,…, an,an=an−1+an−2 for all values

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Senior Manager
Senior Manager
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Joined: 21 Oct 2013
Posts: 451
Followers: 11

Kudos [?]: 681 [0], given: 289

For the sequence a1,a2,a3,…, an,an=an−1+an−2 for all values [#permalink] New post 28 Feb 2014, 09:49
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For the sequence a1,a2,a3,…, an,an=an−1+an−2 for all values n>2. If a1=1 and a3=4, what are the values of a2 and a8?

a2 a8
2
3
29
47
76

OE
[Reveal] Spoiler:
The second term in this sequence should be convenient to calculate, as you're given the first and third terms, 1 and 4, and told that each term is the sum of the two preceding terms. So 1 + a2 needs to equal 4, making a2=3. From there, you can continue to add terms until you reach the 8th term:
1st: 1
2nd: 3
3rd: 4
4th: 7
5th: 11
6th: 18
7th: 29
8th: 47

Q from Veritas Prep

Hi, I used the same method as OE. Can anyone know other faster way to solve this question, please.
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Magoosh GMAT Instructor
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Kudos [?]: 3182 [1] , given: 38

Re: For the sequence a1,a2,a3,…, an,an=an−1+an−2 for all values [#permalink] New post 28 Feb 2014, 13:19
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goodyear2013 wrote:
For the sequence a1,a2,a3,…, an,an=an−1+an−2 for all values n>2. If a1=1 and a3=4, what are the values of a2 and a8?

a2 a8
2
3
29
47
76

Hi, I used the same method as OE. Can anyone know other faster way to solve this question, please.

Dear goodyear2013,
I'm happy to respond. :-)

First of all, do you understand the problem in the way you wrote the question? For example, "an−1" could mean (an) - 1, but I happen to be familiar with this sequence, so I knew that you meant a(n - 1). This mistake indicates a lack of understanding of mathematical grouping symbols, and this gap in your understanding could cause problems on the test. See:
http://magoosh.com/gmat/2013/gmat-quant ... g-symbols/

As to you question: the short answer is "no." With recursive series, the only way we have to get to, say, the 8th term, is to calculate each individual term from 1 to 8, because each one depends uniquely on the ones before it. With arithmetic or geometric series, we can compute the general nth term, but this is not possible for recursive series. See:
http://magoosh.com/gmat/2012/sequences-on-the-gmat/

Does all this make sense?
Mike :-)
_________________

Mike McGarry
Magoosh Test Prep

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Re: For the sequence a1,a2,a3,…, an,an=an−1+an−2 for all values   [#permalink] 28 Feb 2014, 13:19
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For the sequence a1,a2,a3,…, an,an=an−1+an−2 for all values

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