TMUA Practice Question — Worked Solution

P2·Sequences & Series·6.5Mock 0 · P2 · Q19

recurrenceperiodic sequenceundefined termsexact set of valuesextraneous root

A sequence is defined by

u_{1} = a, u_{2} = 2, u_{n + 2} = \frac{u _{n + 1} + 1}{u _{n}} for n \geq 1,

where

a

is a real number.For which values of

a

u_{2029}

defined and equal to

u_{1}

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