Page 31 - Mathematics Class - X

ACTIVITY 2.6

OBJECTIVE
To find the sum of first n odd natural numbers.

MATERIALS REQUIRED

Chart paper
Geometry box, sketch pens, a pencil and adhesive
Graph paper

PRE-REQUISITE KNOWLEDGE
1. Concept of odd natural numbers
2. Area of a square

THEORY
1. Natural numbers which are not completely divisible by 2 are called odd numbers.
i.e. 1, 3, 5, 7, ……..
2. Arithmetic progression is a sequence of numbers such that the difference between the consecutive terms is
constant.

3. The series of odd numbers 1, 3, 5, 7, …….. is an AP with a = 1 and d = 2.
n
4. For an AP, sum of its n terms, S = [2a + (n – 1)d]
n 2
n
Hence, sum for first n odd natural numbers, S = [2 × 1 + (n – 1)2] = n 2
n 2
PROCEDURE

1. Take a graph paper of 10 × 10 cm as shown in Fig. (a).
2. To represent 1, shade top left corner square in red colour as shown in Fig. (b).

Fig. (a) Fig. (b)
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