Consider a sequence {an} with a1=2 and an=a2n−1an−2for all n≥3, terms of the sequence being distinct. Given that a2 and a5 are positive integers and a5≤162 then the possible value(s) of a5 can be
A
164
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B
62
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C
32
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D
2
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Solution
The correct option is C32 Given: a1=2anan−1=an−1an−2
So the sequence is in G.P.
Let a2=x,
Then the common ratio will be, r=x2
So, a5≤162⇒2(x2)5−1≤162⇒x48≤162⇒x≤6
As a2 and a5 are integers ,
For x and x48 to be integers, x=4,6[∵x≠2 as terms are distinct] a5=448,648⇒a5=32,162