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In Example 64, a_{8} equals

Option: 1

21


Option: 2

34


Option: 3

38


Option: 4

41


Answers (1)

best_answer

If \mathrm{ \# (S)=} number of elements of \mathrm{ S}, then

\mathrm{ a_{1}=1, a_{2}=\#\{10,11\}=2}
\mathrm{a_{3}=\#\{101,110,111\}=3}

Next, \mathrm{a_{n}=b_{n}+c_{n}=a_{n-1}+a_{n-2} \forall n \geq 3},
 
we get  \mathrm{a_{4}=a_{3}+a_{2}=5},
             \mathrm{a_{5}=a_{4}+a_{3}=8, a_{6}=13, a_{7}=21}

and       \mathrm{a_{8}=34}
            
    

Posted by

Gautam harsolia

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