0Q 1).Express 49 as a sum of 7 odd numbers
- To solve this we first see 49=7^2
So if we add 1+3+5+7+9+11+13, we get 49
Q.2)Express 121 as a sum of 11 odd numbers
- We see 121=11^2, So if we add first 11 odd numbers starting from 11 we get 121.
So 1+3+5+7+9+11+13+15+17+19+21,we get 121
Without adding, find the sum.
(i) 1 + 3 + 5 + 7 + 9
(ii) 1 + 3 + 5 + 7 + 9 + I1 + 13 + 15 + 17 +19
(iii) 1 + 3 + 5 + 7 + 9 + 11 + 13 + 15 + 17 + 19 + 21 + 23
The general pattern is when we add consecutive odd numbers starting from 1,the sum is square of number of odd numbers.
So (i) sum is 5^2=25
(ii)Here consecutive odd numbers=10, so sum is 10^2=100
(iii) Here consecutive odd numbers=12,so sum is 12^2=144
