Question

If the 3rd and 6th terms of an AP are 7 and 13 .find the first and the common difference.​

Answer 1

Answer:

a=3

d=2

Step-by-step explanation:

nth=a+(n-1)d

3rd=a+2d

6th=a+5d

a+2d=7

a+5d=13

-3d=-6

d=2

a+2(2)=7

a=3

Answer 2

Answer :

first term, a = 3

common difference, d = 2

Step-by-step explanation :

nth term of an AP is given by,

 aₙ = a + (n - 1)d

where

a is the first term

d is the common difference

• 3rd term = 7

  a₃ = a + (3 - 1)d

  7 = a + 2d  -- [1]

• 6th term = 13

  a₆ = a + (6 - 1)d

  13 = a + 5d  -- [2]

equation [2] - equation [1]

 a + 5d - (a + 2d) = 13 - 7

 a + 5d - a - 2d = 6

        3d = 6

          d = 6/3

          d = 2

Therefore, common difference = 2

Substitute d = 2 in equation [1]

  a + 2d = 7

 a + 2(2) = 7

  a + 4 = 7

  a = 7 - 4

  a = 3

So, first term = 3

     

∴ a = 3 , d = 2