NCERT Solutions Ganita Prakash Chapter 1 In-text Questions — Relations among Number Sequences

Book page 7 Updated on2026-09-05

Q1.

By drawing a similar picture, can you say what is the sum of the first 10 odd numbers?

Answer

Adding odd numbers starting from 1 always gives a square number, and the answer is the square of how many odd numbers you added.

A 6 × 6 square of dots split into bent “L” layers of 1, 3, 5, 7, 9 and 11 dots. This is why 1 + 3 + 5 + 7 + 9 + 11 = 36.

Here we are adding the first 10 odd numbers, so the picture is a 10 × 10 square:

1 + 3 + 5 + 7 + 9 + 11 + 13 + 15 + 17 + 19 = 10 × 10 = 100

Answer: 100.

Q2.

Now by imagining a similar picture, or by drawing it partially, as needed, can you say what is the sum of the first 100 odd numbers?

Answer

We do not have to draw all the dots — the rule is now clear. The sum of the first n odd numbers is n × n. So for 100 odd numbers we imagine a 100 × 100 square:

1 + 3 + 5 + … + 197 + 199 = 100 × 100 = 10 000

Answer: 10,000.

The big idea: the picture is not just decoration. Because such a square can be drawn for any size, the picture proves the pattern goes on forever — for 10, for 100, for a million odd numbers.

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