The sum of the series 1⋅3⋅5+2⋅5⋅8+3⋅7⋅11+… up to n terms is

Let, Sn=1⋅3⋅5+2⋅5⋅8+3⋅7⋅11+…+nth term ∴ Tn=n(2n+1)(3n+2)∴ Sn=ΣTn=Σn(2n+1)(3n+2)=Σn6n2+7n+2=Σ6n3+7n2+2n=6Σn3+7Σn2+2Σn=6n(n+1)22+7n(n+1)(2n+1)6+2n(n+1)2=n(n+1)26n(n+1)2+7(2n+1)3+2=n(n+1)218n2+n+28n+14+126=n(n+1)218n2+46n+266=n(n+1)2×29n2+23n+136=n(n+1)9n2+23n+136