Residue of a sequence

Probability Level 2

Consider a sequence {ai}\{a_i\} of positive integers defined by a1=1,a2=2a_1= 1, a_2= 2, and for all integers n>2n>2, an=3an1+5an2a_n= 3a_{n-1} + 5a_{n-2} Consider the set S={a1,a2,,a1200}S= \{a_1, a_2, \cdots , a_{1200} \} Sam randomly picks an element from this set. The probability that this element is a multiple of 88 can be expressed as ab\dfrac{a}{b}, where a,ba, b are coprime positive integers. Find a+ba+b.

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