# 7.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

We know that the sum of n odd numbers =$$n^2$$.So, we have:
(i) 1 + 3 + 5 + 7 + 9 = $$(5)^2$$ = 25 [∵ n = 5]
(iii) 1 + 3 + 5 + 7 + 9 + 11 + 13 + 15 + 17 + 19 + 21 + 23 = $$(12)^2$$ = 144 [∵ n = 12]