find the sum of the n terms of the series (3)(5)+(4)(7)+(5)(9)+---------------------

apply the airthmatic and geometric progression concept....!

3,4,5 ... are in A.P

a=3,d=1

nth term of A.p=n+2

5,7,9 ...are in A.P

a=5,d=2

nth term of A.P=2n+3

nth term of given series=(n+2)*(2n+3)

sum of given series=sigma[(n+2)*(2n+3)]

                          =n/6(4n^2+9n+41)

please approved my answer.