QUESTIONS 9 AND 10 REQUIRE WRITTEN SOLUTIONS WHICH MAY INCLUDE PROOFS....

9. A sequence is formed by the following rules: s

1

=a, s

2

=bands

n+2

=s

n+1

+ (−1)

ⁿ

s

ⁿ

for alln≥1.Ifa= 3 andbis an integer less than 1000, what is the largest value ofbfor which 2015 is a member of the sequence?Justify your answer. [5 marks]