Q3 of 239 Page 29

Find the sum of the following numbers without actually adding the numbers.
1 + 3 + 5 + 7 + 9 + 11 + 13 + 15

We know that the sum of first n odd numbers is n²

Since there are 8 odd numbers starting from 1 to 15,

Sum = 8²

= 64

Write down the unit digits of the following:

35²

Write down the unit digits of the following:

42²

Find the sum of the following numbers without actually adding the numbers.

1 + 3 + 5 + 7

Find the sum of the following numbers without actually adding the numbers.

1 + 3 + 5 + 7 + 9 + 11 + 13 + 15 + 17

Questions · 239

1. Real Number System

1 1 1 1 1 2 2 2 2 2 3 3 3 3 3 4 4 5 5 6 6 1 1 1 1 2 2 2 2 3 3 3 3 1 1 1 1 1 2 2 2 2 2 2 2 2 1 1 1 1 1 1 1 1 1 1 2 2 2 2 2 2 2 2 2 2 3 3 3 3 3 3 4 4 4 4 4 4 5 5 6 6 1 2 2 2 2 2 3 3 3 4 4 4 4 5 5 5 5 5 6 6 6 6 6 6 7 7 1 1 1 1 2 2 2 2 3 3 3 3 3 3 3 3 3 3 4 4 4 4 4 4 4 4 4 4 5 5 5 5 5 5 5 5 6 6 6 6 6 7 7 7 7 7 8 8 8 8 8 9 10 10 10 10 1 1 1 1 1 1 1 1 1 1 2 2 2 2 2 2 3 3 3 3 3 3 4 4 4 4 4 4 5 5 5 5 5 6 6 6 6 6 6 6 6 7 1 1 1 1 1 1 2 2 2 2 2 2 3 3 3 3 3 3 4 4 4 4 4 4 1 1 1 1 1 1 1 2 3

Find the sum of the following numbers without actually adding the numbers.1 + 3 + 5 + 7 + 9 + 11 + 13 + 15