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

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

for integers n>=2.

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

we have a_n < (7/4)ⁿ.

Be sure to lay out your proof clearly and correctly.