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 nth term of A.P. is
an = a1 + ( n - 1 ) d
Here a1 = first term , n = number of terms and d = common difference
And as given 3rd term of A.P. is 13
So,
13 = a1 + ( 3 - 1 ) d
a1 + 2d = 13 --------- ( 1 )
And
Given 7th 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,
nth term of this A.P. is
an = 3 + ( n - 1 ) 5
an = 3 + 5 n - 5
an = 5 n - 2 ( Ans )
We know formula for nth term of A.P. is
an = a1 + ( n - 1 ) d
Here a1 = first term , n = number of terms and d = common difference
And as given 3rd term of A.P. is 13
So,
13 = a1 + ( 3 - 1 ) d
a1 + 2d = 13 --------- ( 1 )
And
Given 7th 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,
nth term of this A.P. is
an = 3 + ( n - 1 ) 5
an = 3 + 5 n - 5
an = 5 n - 2 ( Ans )