Page 25 - Mathematics Class - X

ACTIVITY 2.4

OBJECTIVE
To identify arithmetic progressions in some given lists of numbers (patterns).

MATERIALS REQUIRED

Cardboard

White paper
Pen/Pencil
Scissors

Squared (graph) papers
Glue

PRE-REQUISITE KNOWLEDGE
Concept of Arithmetic Progression

THEORY
1. In the list of numbers a , a , a , a ,... if the differences a – a , a – a , a – a ,... give the same value are said
1
2
1
3
2
3
4
2
4
3
to make arithmetic progression.
2. The general form of an AP is a, a + d, a + 2d, a + 3d
where, a is the first term and d is the common difference.
3. nth term of an AP; T = a + (n – 1)d
n
PROCEDURE
1. Take a cardboard of a suitable size and paste a white paper on it.
2. Take two squared papers of suitable size and paste them on the cardboard.

3. Let the numbers of list are:

(i) 1, 2, 5, 9, .......
(ii) 2, 5, 8, 11, ......

4. Make strips of lengths 1, 2, 5, 9 units, strips of lengths 2, 5, 8, 11 units, each having breadth one unit.

5. Paste the strips of lengths 1, 2, 5, 9 units as shown in Fig. (a).
6. Paste the strips of lengths 2, 5, 8, 11 units as shown in Fig. (b).

7. In Fig. (a), the difference of heights (lengths) of two consecutive strips is not uniform. So, it is not an AP.

8. In Fig. (b), the difference of heights of two consecutive strips is uniform throughout, so, it is an AP.

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