Question

Without adding find the sum

1. $1 + 3 + 5 + 7 + 9$
2. $1 + 3 + 5 + 7 + 9 + 11 + 13 + 15 + 17 + 19$
3. $1 + 3 + 5 + 7 + 9 + 11 + 13 + 15 + 17 + 19 + 21 + 23$

Answer 1

We know that the sum of first n odd natural numbers is $n^2$.
(i) Here, we have to find the sum of first five odd natural numbers.
Therefore, $1 + 3 + 5 + 7 + 9 = (5)^2= 25$

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(ii) Here, we have to find the sum of first ten odd natural numbers.
Therefore, $1 + 3 + 5 + 7 + 9 + 11 + 13 + 15 + 17 + 19 = (10)^2= 100$

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(iii) Here, we have to find the sum of first twelve odd natural numbers.
Therefore, $1 + 3 + 5 + 7 + 9 + 11 + 13 + 15 +17 + 19 + 21 + 23 = (12)^2= 144$