a3=4=2^2

a2+a4=2

a3

a4=6

a3×a5=a4^2

a5=9=3^2

The nth term in bn is a2n- 1.

A2n-2, A2n- 1, A2n becomes arithmetic progression.

The tolerance is n.

a2n- 1=a2n-n

A2n, a2n+ 1, a2n+2 make arithmetic progression.

The tolerance is n+ 1.

a2n= 1=a2n

+n+ 1

A2n- 1, A2n, a2+ 1 into geometric series.

a2n^2=(a 2n-n)*(a2n+n+ 1)

Simplified a2n = n 2+n

So a2n- 1 = a2n-n = n 2.

So bn = n 2