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# In a sequence, after the first two terms, each term is the

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Senior Manager
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In a sequence, after the first two terms, each term is the [#permalink]

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21 Apr 2006, 03:17
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In a sequence, after the first two terms, each term is the sum of all the previous terms. If an=P, a(n+2)=?

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Director
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21 Apr 2006, 04:33
a(1) = a
a(2) = b
a(3) = a+b
a(4) = 2a + 2b
a(5) = 4a + 4b

Let us take a(n) = a(3) = a + b = P
Therefore, a(n+ 2) = a(5) = 4(a+b) = 4P

Ans = 4P

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VP
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27 Apr 2006, 20:12
Agree with remgeo's approach
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Don't be afraid to take a flying leap of faith.. If you risk nothing, than you gain nothing...

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Manager
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28 Apr 2006, 06:05
remgeo wrote:
a(1) = a
a(2) = b
a(3) = a+b
a(4) = 2a + 2b
a(5) = 4a + 4b

Let us take a(n) = a(3) = a + b = P
Therefore, a(n+ 2) = a(5) = 4(a+b) = 4P

Ans = 4P

Took me a while but I think i understand your explanation.

since we let n=3, a(3)= a+b
therefore, P= a+b
Now lets look at a(n+2), since n=3 we have a(3+2)=a(5), where a(5)= 4a+4b. or 4(a+b), since P=a+b, we have 4P

I had to break it down for my understanding, plz let me know if I am wrong. greak work!

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Director
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29 Apr 2006, 08:40
Does it work for n=1?

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Manager
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29 Apr 2006, 09:15
Probably the question is interested in all n after the first two numbers.
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Thanks,
Zooroopa

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29 Apr 2006, 09:15
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# In a sequence, after the first two terms, each term is the

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