Multiply both sides by 2 (n+ 1)

Get 2 (n+1) a (n+1) = 2n× an+1.

Let BN = 2 n× an, then b (n+1) = 2 (n+1) a (n+1), b1= 21=

Then b(n+ 1)=bn+ 1.

That is, b(n+ 1)-bn= 1.

Then {bn} is arithmetic progression, with tolerance d= 1 and b 1=5/3.

Therefore, bn = b1+() d = 5/3+(n-1) ×1= n+2/3 = (3n+2)/3.

And bn = 2 n× an

We know that an = bn/2n = [(3n+2)/3]/2n = (3n+2)/3× 2n.