The A.M. of first n terms of the series 1.3.5, 3.5.7, 5.7.9,....., is
∵Tn=(2n−1)(2n+1)(2n+3)
Req. A.M.
=Snn=∑Tnn=1n[∑(8n3+12n2−2n−3)]
=1n[8∑n3+12∑n2−2∑n−∑3]
=2n3+8n2+7n−2
The arithmetic mean (A.M.) of the observations 1.3.5, 3.5.7, 5.7.9...(2n–1).(2n+1).(2n+3) is