Question

The 4th term of an A.p. is three times the first and 7th term exceeds twice the third term by 1. find the first term and the common difference​

Answer 1

Answer:

let first term of A.P.=a

and common difference=d

we know that nth term of A.P.=first term +(n-1)*common difference

4th term=a+3*d = 3a

               3d=2a

                 d=2a/3       -------- (1)

 7th term=a+6d=2*third term + 1 =2*(a+2d) +1

                =a+6d=2a+4d+1

                2d=a+1

        from equation 1

        2*(2a/3)=a+1

       4a/3 = a+1

        4a/3 - a=1

         a/3 =1

          a=3

  from equation 1

 d=2*3/3

d=2