Q. 144.3( 9 Votes )

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

Answer :

Since the sum of n terms is

S_{n =} …(i)

Where,

a = First term of AP

d = Common difference of AP

and no of terms is ‘n’

Also S_{n} =

⇒ S_{n} =

⇒ S_{n} =

⇒ S_{n} =

⇒ S_{n} = …(ii)

On comparing eq. (i) and (ii), we get:

a = 4 and d = 3

Also, n^{th} term a_{n} is given by:

a_{n} = a + (n – 1)d

For given AP, we have

a_{n} = 4 + (n - 1)6

⇒ a_{25} = 4 + (25 - 1) × 3

⇒ a_{25} = 4 + 24 × 3

⇒ a_{25} = 4 + 72

⇒ a_{25} = 76

Hence, 25^{th} term is 76.

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