Q14 of 67 Page 74

If the sum of a terms of an arithmetic progression is then find its 25th term.

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 =
⇒ Sn =
⇒ Sn =
⇒ Sn =
⇒ Sn = …(ii)


On comparing eq. (i) and (ii), we get:
a = 4 and d = 3


Also, nth term an is given by:
an = a + (n – 1)d


For given AP, we have


an = 4 + (n - 1)6
⇒ a25 = 4 + (25 - 1) × 3
⇒ a25 = 4 + 24 × 3
⇒ a25 = 4 + 72
⇒ a25 = 76


Hence, 25th term is 76.


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