# 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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