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Question:

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

Solution:

(i) 1+3+5+7+9
Since, there are 5 consecutive odd numbers, Thus, their sum = 5² = 25
(ii) 1+3+5+7+9+11+13+15+17+19
Since, there are 10 consecutive odd numbers, Thus, their sum = 10² = 100
(iii) 1+3+5+7+9+11+13+15+17+19+21+23
Since, there are 12 consecutive odd numbers, Thus, their sum = 12² = 144.