Question

Let an 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 bn = the number of such n digit integers ending with digit 1 and cn = the number of such n digit integers ending with digit 0. the value of b^6 is??

Answer 1

Answer:

8

Step-by-step explanation:

an = bn + cn

also,  bn = a(n-1) and an = a(n-1) + a(n-2)

as a1 =1 and a2 = 2,

so, a3 = 3 a4=5 and a5 = 8

using bn =a(n-1),

b6 = a5 = 8 (this is the correct answer as per JEE 2012 paper 2 official marking scheme)

Hope that helps!