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Question

Without adding, find the sum:
(i) (1 + 3 + 5 + 7 + 9 + 11 + 13)
(ii) (1 + 3 + 5 + 7 + 9 + 11 + 13 + 15 + 17 + 19)
(iii) (1 + 3 + 5 + 7 + 9 + 11 + 13 + 15 + 17 + 19 + 21 + 23)

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Solution

Sum of first n odd numbers = n2

(i) (1+3+5+7+9+11+13) = 72=49

(ii) (1+3+5+7+9+11+13+15+17+19)=102=100

(iii) (1+3+5+7+9+11+13+15+17+19+21+23) = 122 = 144

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