The solution of the recurrence relation is 
For given question,
We have been given a recurrence relation
for n ≥ 1
and an initial condition 
Let
= m²,
= m and
= 1
So from given recurrence relation we get an characteristic equation,
⇒ m² = 2m
⇒ m² - 2m = 0 .........( Subtract 2m from each side)
⇒ m(m - 2) = 0 .........(Factorize)
⇒ m = 0 or m - 2 = 0
⇒ m = 0 or m = 2
We know that the solution of the recurrence relation is then of the form
where
are the roots of the characteristic equation.
Let,
= 0 and
= 2
From above roots,

For n = 0,

But 
This means 
so, the solution of the recurrence relation would be 
Therefore, the solution of the recurrence relation is 
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