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What can you say about the sum of fibonacci numbers till 2017

Source: MTRP 2017 Class 11-Multiple Choice Question: Problem 4 :-

May 25, 2020
Fibonacci sequencealgebra

Problem Statement

Let F1=F2=1F_1=F_2=1. We define inductively Fn+1=Fn+Fn−1F_{n+1}=F_n+F_{n-1} for all n≥2n\geq 2. Then the sum F1+F2+⋯+F2017F_1+F_2+\cdots+F_{2017} is
[*] Even but not divisible by 3 [*] Odd but divisible by 3 [*] Odd and leaves remainder 1 when divisible by 3 [*] None of these
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