JEE Advanced · 2012 · 08 Apr 2012 · Paper 2 · Sequences and Series

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.

Which of the following is correct?

(A) $a_{17} = a_{16} + a_{15}$ ✓ Correct
(B) $c_{17} \neq = c_{16} + c_{15}$
(C) $b_{17} \neq = b_{16} + c_{16}$
(D) $a_{17} = c_{17} + b_{16}$

Answer: (A)

Solution

From the recurrence relation derived in the previous question:

a_{n} = a_{n - 1} + a_{n - 2}

For

n = 17

a_{17} = a_{16} + a_{15}

.

This is the correct relation.

JEE Advanced · 2012 · 08 Apr 2012 · Paper 2 · Single correct option

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