Answer :

Now, Sum of n terms

⇒

=

= n[5 + 2n–2]

=n[3 + 2n]

Now,

⇒

=

= (n + 1)[7 + n]

⇒

On cross multiplying we get,

16n[3 + 2n] = 17n + 17[7 + n]

⇒ 48n + 32n^{2} = 119n + 17n^{2} + 119 + 17n

⇒ 48n + 32n^{2} = 136n + 17n^{2} + 119

⇒ 15n^{2} – 88n – 199 = 0

⇒ n =

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The sum of n terms of an A.P. is 3n^{2}+ 5n. Find the A.P. Hence, find its 16th term.