Q5 of 67 Page 74

If the sum of n terms of an arithmetic progression in 3n2 + 5n, then which term of its is 164:

Since the sum of n terms is
Sn = …(i)


Where,


a = First term of AP
d = Common difference of AP
and no of terms is ‘n’



Also Sn = 3n2 + 5n
⇒ Sn = n(3n + 5)
⇒ Sn = n(3n + 8 - 3)
⇒ Sn = n[8 + 3(n -1)]
⇒ Sn = n[8 + (n - 1)3]
⇒ Sn …(ii)


On comparing eq. (i) and (ii), we get :
a = 8 and d = 6


Since, nth term an is given by :


an= a + (n – 1)d


Where,


a = First term of AP
d = Common difference of AP
and no of terms is ‘n’



an = 8 + (n - 1)6
⇒ 164 = 8 + (n - 1) × 6
⇒ 156 = (n - 1) × 6
⇒ (n - 1) = 26
⇒ n = 27.

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