Without adding, find the sum.
(i) 1 + 3 + 5+ 7+ 9
(ii) 1 + 3 + 5 + 7 + 9 + 11 + 13 + 15 + 17 + 19
(iii) 1 + 3 + 5 + 7 + 9 + 11 + 13 + 15 + 17 + 19 + 21 + 23
(i) The sum of first 5 odd numbers = 52
= 25
(ii) The sum of first 10 odd numbers = 102
= 100
(iii) The sum of first 12 odd numbers = 122
= 144
Express 49 as the sum of 7 odd numbers.
49 = 72 = Sum of first 7 odd numbers
= 1 + 3+ 5 +7 +9 + 11 + 13
How many numbers lie between squares of the following numbers?
(i) 12 and 13 (ii) 25 and 26 (iii) 99 and 100
Since between n2 and (n + l)2, there are 2n non-square numbers.
∴ (i) Between 122 and 132, there are 2 × 12, i.e. 24 numbers
(ii) Between 252 and 26:, there are 2 × 25, i.e. 50 numbers
(iii) Between 992 and 1002, there are 2 × 99, i.e. 198 numbers
Using the given pattern, find the missing numbers.
12+22 +22 = 32
22+32 +22 = 62
32+42 +122 = 132
42+52 +___2 = 212
52+__2 +302 = 312
62+72+___2 =_____2
Note: To find pattern:
Third number is related to first and second number. How?
Fourth number is related to third number. How?
The missing numbers are
(i) 42 + 52 + 202 = 212 (ii) 52 + 62 + 302 = 312
(iii) 62 + 72 + 422 = 43
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