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.