Question: Define a sequence a 1 , a 2 , a 3 , ... as follows: a 1 = 1, a 2 = 3, and a

Define a sequence a1, a2, a3, ... as follows:

a1 = 1, a2 = 3, and an+1 = an-1 + an

for integers n>=2.

Use strong mathematical induction to prove that for all integers n>=1,

we have an < (7/4)n.

Be sure to lay out your proof clearly and correctly.

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