Without adding, find the sum in the following:
(i) 1 + 3 + 5 + 7 + 9 +11+13
(ii) 1 + 3 + 5 + 7 + 9 +11+13+15+17+19+21+23+25+27+29+31
[3 marks]

(i) We know that the sum of first 'n' odd natural numbers is equal to <!--td {border: 1px solid #ccc;}br {mso-data-placement:same-cell;}--> $n^2$
[1 mark]

Now first 7 odd natural numbers are added,
Therefore, 1 + 3 + 5 + 7 + 9 +11+13 = $7^2$ = 49
[1 mark]


(ii) We know that the sum of first 'n' odd natural numbers is equal to <!--td {border: 1px solid #ccc;}br {mso-data-placement:same-cell;}--> $n^2$
Now first 16 odd natural numbers are added,
Therefore, 1 + 3 + 5 + 7 + 9 +11+13+15+17+19+21+23+25+27+29+31 = ${16}^2$ = 256
[1 mark]