Find the sum of the first 25 terms of the following series whose n^th term is given:

a_n = 3 + 4n

General n^th term a_n is given as:
a_n = a + (n - 1)d … (i)

Where,

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

and a_n = 3 + 4n
⇒ a_n = (7-4) + 4n
⇒ a_n = 7 + 4n – 4
⇒ a_n = 7 + 4(n – 1)
⇒ a_n = 7+ (n – 1)× 4 …(ii)

On comparing eq. (i) and (ii), we get,
a = 7 and d = 4

Here first term is 7 and common difference is 4.
Since the sum of n terms is
S_{n =}

Where,

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

So sum of first 25 terms S₂₅
= 12.5 × [ 14 + 24×4]
= 12.5 × [ 14 + 96]
= 12.5 × 110
= 1375

Hence, Sum of first 25 terms is 1375.