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A sequence is given by the rule a_{n+2}= 2/a_{n+1}+a_n, n is a positi

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A sequence is given by the rule a_{n+2}= 2/a_{n+1}+a_n, n is a positi [#permalink] A sequence is given by the rule a_{n+2}= 2/a_{n+1}+a_n, n is a positi   31 Oct 2019, 09:05
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A sequence is given by the rule

\(a_{n+2}=\frac{2}{a_{n+1}} +a_n\), where n>0. Also, \(a_1\)=1 and \(a_2\)=2.

Find the value of \(a_{100}*a_{101}\)?

A. 80
B. 120
C. 160
D. 200
E. 240
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Peddi
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Re: A sequence is given by the rule a_{n+2}= 2/a_{n+1}+a_n, n is a positi [#permalink] A sequence is given by the rule a_{n+2}= 2/a_{n+1}+a_n, n is a positi   31 Oct 2019, 09:43
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A101=(2/A100)+A99. ..>A100*A101=2+A99.A100=2+2+A98.A99.....the sequence follows the final answersA100.A101=2*100=200

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Re: A sequence is given by the rule a_{n+2}= 2/a_{n+1}+a_n, n is a positi [#permalink] A sequence is given by the rule a_{n+2}= 2/a_{n+1}+a_n, n is a positi   25 May 2024, 22:32
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Can somebody explain this question with solution

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Re: A sequence is given by the rule a_{n+2}= 2/a_{n+1}+a_n, n is a positi [#permalink] A sequence is given by the rule a_{n+2}= 2/a_{n+1}+a_n, n is a positi   26 May 2024, 08:58
Anjali_1453 wrote:
Can somebody explain this question with solution

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­a_{n+2} a_{n+1}-a_{n+1}a_{n}=2

put n=1,2,3,...99:
a3a2-a2a1=2
a4a3-a3a2=2
..
.
a101a100-a100a99=2

add it up:
a101a100-a2a1=2(99)
=> a101a100=198+2=200
 
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Re: A sequence is given by the rule a_{n+2}= 2/a_{n+1}+a_n, n is a positi [#permalink]
26 May 2024, 08:58
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