Question

if 7, a ,b, 22 are the consecutive terms of an arithmetic Progression, then the values of a and b are respectively equal to ,
a) 11 and 16
b) 12 and 17
c) 13 and 17
d) 12 and 16​

Answer 1

Answer:

Ans is Opt b

Step-by-step explanation:

a=7

d=5

a , a+d ,a+2d , a+3d

Answer 2

Answer:

The values of a and b are 12 and 17 respectively.

Option(b) is correct.

Step-by-step explanation:

• Given arithmetic progression is  

           7, a, b, 22

     so we can write

      first term a₁=7

      second term =a₂=a₁+d=a  

      third term =a₃=a₂+d=b

       fourth term =a₄=a₃+d= 22

Consider

       a₁+d=a   -----------(i)

       a₂+d=b  -----------(ii)

By solving above two equations we get

    a₁-a₂ = a-b  ------(iii)

Now consider

      a₂+d=b  -----------(iv)

      a₃+d= 22----------(v)

By solving above two equations we get

      a₂-a₃ = b-22  --------(vi)

now by solving equation (iii) and (vi) we get

       a₁-a₃ = a-22

       now substitute a₁=7 and a₃=a₂+d in the above equation

          7-(a₂+d )=a-22

        as we have a₂=a

          7-(a+d) = a-22

       from second term we can write d=a-7

         7-(a+a-7) = a-22

            7-2a+7 = a-22

             14-2a-a+22 = 0

             14+22-3a=0

                        3a= 36

                        a=12

Hence the second term = a₂=a=12

              Since a₁+d=a  and a₁=7, a=12

             substitute a₁=7and a=12 in a₁+d=a

                   7+d=12

                       d=12-7

                       d=5  

     now we can find the third term a₃=a₂+d=b

                a₃=12+5= 17

        Hence b= 17

   Therefore the values of a and b are 12 and 17 respectively.

Know more about Arithmetic progression:

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