## ‘0’ and ‘1’ only but no two consecutive Zero

Let  $a_{n}$ denote the number of all n-digit positive integers formed bt the digit ‘0’ and ‘1’ or both such that no consecutive digits in them are 0. Let  $b_{n}$ = the number of such n-digit integers ending with digit 1 and  $c_{n}$ = the number of such n-digit integers ending with digit 0

Which of the following is correct ?

(A) $a_{17}=a_{16}+a_{15}$

(B)  $c_{17}=|c_{16}+c_{15}$

(C) $b_{17}=|b_{16}+c_{16}$

(D) $a_{17}=c_{17}+b_{16}$

What is the value of $b_{6}$

(A) 7

(B) 8

(C) 9

(D) 11

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