JEE Advanced 2019 Paper 1 Mathematics Q5

Mathematics

Problem

Let α and β be the roots of x² − x − 1 = 0, with α > β. For all positive integers n, define aₙ = (αⁿ − βⁿ)/(α − β), n ≥ 1, b₁ = 1 and bₙ = aₙ₋₁ + aₙ₊₁, n ≥ 2. Then which of the following options is/are correct?

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