Answer :

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 S_{25}

= 12.5 × [ 14 + 24×4]

= 12.5 × [ 14 + 96]

= 12.5 × 110

= 1375

Hence, Sum of first 25 terms is 1375.

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