Fibonacci hype!

Number Theory Level 2

Let g 0 , g 1 , g 2 , . . . g n g_{0},g_{1},g_{2},...g_{n} be a sequence satisfying the Fibonacci recurrence relation such that g n = g n − 1 + g n − 2 g_{n}=g_{n-1}+g_{n-2} g 0 = 2 , g 1 = − 1 g_{0}=2, g_{1}=-1 where 2 ≤ n 2\leq n Find g 6 g_{6} without using brute force.


The answer is 2.

Marc Vince Casimiro by Marc Vince Casimiro , 22, Philippines

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2 solutions

Jyotsna Sharma
Dec 1, 2014

g(2)=g(1)+g(0)=2-1=1 given that it satisfies fibonacci recurrence relation the series becomes---->2,-1,1,0,1,1,2.......... g(6)=2

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Aayush Patni
Dec 1, 2014

g(2)=g(1)+g(0) = -1+2 = 1

g(6)=g(5)+g(4) = g(4)+g(3)+g(3)+g(2)

= g(3)+g(2)+g(2)+g(1)+g(2)+g(1)+g(2)

= g(2)+g(1)+g(2)+g(2)+g(1)+g(2)+g(1)+g(2)

= 1-1+1+1-1+1-1+1

= 2

Hope the solution is simple

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