Find the sum of the following series upto n terms 3 × 8 + 6 × 11 + 9 × 14+….

Question

Philoid · Accepted Answer

Here the series is formed by multiplying the corresponding terms of two series both of which are A.P.

Viz. 3, 6, 9 …… and 8, 11, 14…..

Tn of given series

= (nth term of 3, 6, 9,….) × (nth term of 8, 11, 14,….)

= [3 +(n – 1)3] [8 + (n – 1)3]

= [3n][3n + 5]

= 9n2 + 15n

Sn = 9 ∑ n2 + 15∑ n

= 9 × 
    = 
    =  = 3n(n + 1) ( n + 3)