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Let $a_{n}$ denote the number of all $n$-digit positive integers formed by the digits 0,1 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 .
Question: Which of the following is correct?
Options:
Question: Which of the following is correct?
Solution:
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Verified Answer
The correct answer is:
$a_{17}=a_{16}+a_{15}$
By recurring formula, $a_{17}=a_{16}+a_{15}$ is correct
Also $c_{17} \neq c_{16}+c_{15}$
$\Rightarrow a_{15} \neq a_{14}+a_{13}\left(\because c_{n}=a_{n-2}\right)$
$\therefore$ Incorrect
Similarly, other parts are also incorrect.
Also $c_{17} \neq c_{16}+c_{15}$
$\Rightarrow a_{15} \neq a_{14}+a_{13}\left(\because c_{n}=a_{n-2}\right)$
$\therefore$ Incorrect
Similarly, other parts are also incorrect.
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