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  4. If sum of n terms of an AP is 2n2+5n, then its nth term is

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Q. If sum of n terms of an AP is $ 2{{n}^{2}}+5n, $ then its nth term is

Rajasthan PETRajasthan PET 2004

Solution:

Sum of n terms, $ {{S}_{n}}=2{{n}^{2}}+5n $
$ {{T}_{n}}={{S}_{n}}-{{S}_{n-1}} $
$ =2{{n}^{2}}+5n-[2{{(n-1)}^{2}}+5(n-1)] $
$ =2{{n}^{2}}+5n-2{{n}^{2}}-2+4n-5n+5 $
$ =4n+3 $