Page 28 - Mathematics Class - X

ACTIVITY 2.5

OBJECTIVE
To find the sum of first n natural numbers.

MATERIALS REQUIRED

Graph paper A pencil, colour pencils, a ruler and an eraser
A pair of scissors and glue Chart paper

PRE-REQUISITE KNOWLEDGE

1. Concept of natural numbers
2. Areas of squares and rectangles

THEORY
1. Numbers which are used for counting, i.e., 1, 2, 3, 4, …… are called natural numbers.
2. Arithmetic progression (AP) or arithmetic sequence is a sequence of numbers such that the difference
between the consecutive terms is constant.

n
n 1
3. For an AP, sum of its n terms, S = 2 [ a +2 ( – )] d
n
Where, a = first term, d = common difference and n = number of terms
Now, according to the sequence of natural number–

1, 2, 3, 4, ...........

Here, a = 1, d = 1, number of terms = n
n n n
Now, put these data in above formula S = [21 ( n − × ] = [2) + n − ] = [ n + ] 1
11
× +
1
n 2 2 2
PROCEDURE
We will consider the sum of natural numbers, say from 1 to 10,
i.e., 1 + 2 + 3 + ... + 9 + 10.
Here, n = 10 and n + 1 = 11.

1. Take a graph paper of size 10 × 11 squares and paste it on a
chart paper.

2. On the left side vertical line, mark the squares by 1, 2, 3, ..., 10
and on the horizontal line, mark the squares by 1, 2, 3, ..., 11.

3. Shade the rectangles of length equal to 1 cm, 2 cm, ..., 10 cm
and 1 cm width each with colour pencils, as shown in fig. (a).

Fig. (a)

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