Arithmetic progression

As performed in real lab:

Material Required:

Colored paper, Pair of scissors, Geometry box, Fevicol, Sketch paper, One squared paper.

Procedure:

  • Take a given sequence of numbers say a1, a2, a3 ....
  •  Cut a rectangular strip from a coloured paper of width k = 1 cm (say) and length a1 cm.
  • Repeat this procedure by cutting rectangular strips of the same width k = 1cm and lengths a2, a3, a4.. cm.
  • Take 1 cm squared paper and paste the rectangular strips adjacent to each other in order.

            

[A]Let the sequence be 1, 4, 7, 10, ....

  • Take strips of lengths 1 cm, 4 cm, 7 cm and 10 cm, all of the same width say 1 cm.
  • Arrange the strips in order as shown in Fig 1(a).
  • Observe that the adjoining strips have a common difference in heights. (In this example it is 3 cm.)

                                        Figure 1(a)

           

[B]Let another sequence be 1, 4, 6, 9, ...

  • Take strips of lengths 1 cm, 4 cm, 6 cm and 9 cm all of the same width say 1 cm.
  • Arrange them in an order as shown in Fig 1(b).
  • Observe that in this case the adjoining strips do not have the same difference in heights.
     

                                                Figure 1(b)

As performed in the simulator:

 

  • Click on each box provided in workbench area. Here, we will be generating sequence of 1,4,7,10....
  • Click on next button below.
  • Click on each box provided in workbench area. Here, we will be generating sequence of 1,4,6,9....
  • Click on next button below.

 

 

Observation

So, it is observed that if the given sequence is an arithmetic progression, a ladder is formed in which the difference between the heights of adjoining steps is constant. If the sequence is not an arithmetic progression, a ladder is formed in which the difference between adjoining steps is not constant.
 

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