question_answer 1)

                Without adding, find the sum:                 (i) 1 + 3 + 5 + 7 + 9 (ii) 2 + 3 + 5 + 7 + 9 + 22 + 23 + 25 + 27 + 29 (iii) 2 + 3 + 5 + 7 + 9 + 22 + 23 + 25 + 27 + 29 + 21 + 23.

Answer:

                (i) 1 + 3 + 5 + 7 + 9 = sum of first five odd natural numbers = 52 = 25 (ii) 1 + 3 + 5 + 7 + 9 + 11 + 13 + 15 + 17 + 19 = sum of first ten odd natural numbers = 102 = 100 (iii) 1 + 3 + 5 + 7 + 9 + 11 + 13 + 15 + 17 + 19 + 21 + 23 = sum of first twelve odd natural numbers \[={{12}^{2}}=144\].