The third and the seventh term of an A.P. are 13 and 33 respectively. Find nth term of the A.P.

Answer :

We know formula for n^th term of A.P. is

a_n  = a₁  +  ( n  -  1 )  d

Here a₁ =  first term  , n  =  number of terms and d  =  common difference

And as given 3^rd term of A.P. is 13
So,

13  =  a₁ + ( 3  -  1 ) d

a₁ +  2d  =  13                                      --------- ( 1 )

And
Given 7^th term of A.P. is 33
So,

33  =  a₁ + ( 7  -  1 ) d

a₁ +  6d  =  33                                      --------- ( 2 )

Now we subtract equation 1 from equation 2 , we get

4d  = 20

d = 5 , Substitute that value in equation 1 , we get

a₁ + 2 ( 5 ) =  13

a₁ = 13 -  10 = 3

So,

n^th term of this A.P. is

a_n  = 3  +  ( n  -  1 )  5

a_n  = 3  +  5 n  - 5

a_n  = 5 n  - 2                                                                                                                                                        ( Ans )