Is the following statement true or false?If the list

12, 32, 52, 72,...
. is an AP then its common difference is 20 and the next three numbers are 92, 112, and 132.

Question

Is the following statement true or false?If the list

12, 32, 52, 72,...
  .  is an AP then its common difference is 20 and the next three numbers are 92, 112, and 132.

Accepted Answer

Given, the numbers

12, 32, 52, 72,...
  . The formula for common difference,

d=
    a
    n
   
   −
    a

n−1

.The common difference between the first and second term is,

⇒
      a
      2
     
     −
      a
      1
     
     =32−12

⇒
      a
      2
     
     −
      a
      1
     
     =20

The common difference between the second and third term is,

⇒
      a
      3
     
     −
      a
      2
     
     =52−32

⇒
      a
      3
     
     −
      a
      2
     
     =20

The common difference between the third andd fourth term is,

⇒
      a
      4
     
     −
      a
      3
     
     =72−52

⇒
      a
      4
     
     −
      a
      3
     
     =20

We can see that the common difference is the same every time thus, the given numbers form an A.P.Substituting

a
    4

=72 and d=20 in the equation

a
    5
   
   =
    a
    4
   
   +d
  ,

⇒
      a
      5
     
     =72+20

⇒
      a
      5
     
     =92

Substituting

a
    5

=92 and d=20 in the equation

a
    6
   
   =
    a
    5
   
   +d
  ,

⇒
      a
      6
     
     =92+20

⇒
      a
      6
     
     =112

Substituting

a
    6

=112 and d=20 in the equation

a
    7
   
   =
    a
    6
   
   +d
   ,

⇒
      a
      7
     
     =112+20

⇒
      a
      7
     
     =132

Thus the numbers form an A.P with d=20 and the next three terms are 92, 112, and 132.So the given statement is true.Therefore the correct option is 1.

Is the following statement true or false?

If the list $12, 32, 52, 72, ...$ . is an AP then its common difference is 20 and the next three numbers are 92, 112, and 132.

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Is the following statement true or false?If the list 12, 32, 52, 72,... . is an AP then its common difference is 20 and the next three numbers are 92, 112, and 132.