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

Monjur Alahi

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`


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Salim Ahmed Kawsar

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Correct Answer - 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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