Give a recursive definition of the sequence an where an n12

Give a recursive definition of the sequence {a_n} \"where\" a_n = (n+1)²

Solution

Recursive defination means to answer in terms of previous term.

Given:- a_n=(n+1)²

Then, a_n-1=n²

So, we may write an = n₂ + 2n +1

                               = a_n-1 + (2n+1) for n>1 and a₁ = 4

whihc is required recursive form