Page 32 - Mathematics Class - X

3. To represent 1 + 3, shade 3 more squares (in blue colour) adjacent to red square as shown in Fig. (c) (marked
with arrows).
4. To represent 1 + 3 + 5, shade 5 more squares (in green colour) adjacent to previous shaded square as shown
in Fig. (d) (marked with arrows).

Fig. (c) Fig. (d)

5. Keep shading squares with different colours till you represent 1 + 3 + 5 + 7 + 9 + ... + 19
(i.e. sum of first 10 odd natural numbers).

OBSERVATIONS

The number of red squares = 1 = 1 2
The number of red + blue squares = 1 + 3 = 2 2
The number of red + blue + green squares = 1 + 3 + 5 = 3 2

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The number of 1 + 2 + 3 + 4 + ... + 10 squares = 1 + 2 + 3 + 4 + ... + 10 = 10 2

INFERENCE
Hence, the sum of first n odd natural numbers is n .
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EXTENDED TASK
1. Find the sum of first 20 odd numbers using the same method as in activity and verify it by the formula.

2. Divide the class into two groups and name them even and odd numbers or natural and whole numbers.
Debate on how important each classification is.

APPLICATION
The activity is useful in determining formula for the sum of the first n natural numbers.

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