Question: Let (an)n=0 be the sequence defined by the recurrence relation a0=2,a1=2,an=2an1+2an2forn2. Show using induction that an>(25)n for all n2. 1. Qne,could argue that the logic

Let (an)n=0 be the sequence defined by the recurrence relation a0=2,a1=2,an=2an1+2an2forn2.

Show using induction that an>(25)n for all n2. 1. Qne,could argue that

Let (an)n=0 be the sequence defined by the recurrence relation a0=2,a1=2,an=2an1+2an2forn2. Show using induction that an>(25)n for all n2. 1. Qne,could argue that the logic of mathematical induction by application is important in making inferences about computable tasks and the future of such tasks. Provide five example fields of study or professions for which induction is applicable. Explain clearly the reason for your answer. [1, mark]

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