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A fair coin is tossed n times. Let a(n) ...

A fair coin is tossed `n` times. Let `a_(n)` denotes the number of cases in which no two heads occur consecutively. Then which of the following is not true ?

A

`a_(1)=2`

B

`a_(2)=3`

C

`a_(5)=13`

D

`a_(8)=55`

Text Solution

Verified by Experts

The correct Answer is:
C
`(c )` The cases for `a_(1){H,T}` i.e, `a_(1)=2`
The cases for `a_(2){HT,TH,TT}`, `a_(2)=3`
For `n ge 3` , if the first outcome is `H`, then next just `T` and then `a_(n-2)`.
If the first out come is `T`, then `a_(n-1)` should follow.
So, `a_(n)=1xx1xxa_(n-2)+1xxa_(n-1)impliesa_(n)=a_(n-2)+a_(n-1)`
So, `a_(3)=a_(1)+a_(2)=5`, `a_(4)=3+5=8` and so on.
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