Let a₁=24 and form the sequence a_n, n 2 by a_n=100 a_ n-1 +134 . The first few terms are 24,2534,253534,25353534, What is the least value of n for which a _ n is divisible by 99 ?

Step-by-step solution

a₁=24 & a_n=100 . a_ n-1 +134 First few terms : aligned & a₁=24 & a₂=2534 aligned aligned & a₃=253534 & a₄=25353534 & a_n=2 535353 . .534 _ (n-1) Times ^ 53^ aligned Now, an divisible by 99 by 9 & 11 both Sum of digits =6+8(n-1) To be divisible by 9 , n=7,16,25,34,43,52,61,70,79,88, . a ₇=2 535353535353 _ 6 Times ^ 53^ 4 But a ₇ Not divisible by 11 . a ₁₆=2 5353535353 . .53 _ 15 Times'53' 4 Similarly, a ₁₆ Not divisible by 11 . Now, n =88 a ₈₈=2 5353 53 _ 87 Times ^ 53^ 4 aligned & Divisibility by aligned 11 & |(2+