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

a_n = 7 - 3n

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

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

Here first term is 4 and common difference is -3.
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 × [ 8 + 24×(-3)]
= 12.5 × [ 8 - 72]
= 12.5 × (- 64)
= -800

Hence, Sum of first 25 terms is -800.