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 $

Given:

(i) \( 1+3+5+7+9 \)
(ii) \( 1+3+5+7+9+11+13+15+17+19 \)
(iii) \( 1+3+5+7+9+11+13+15+17+19+21+23 \)

To do :

We have to find the sum of the given expressions without adding.

Solution :

We know that,

The sum of 'n' consecutive odd numbers is $n^2$.

(i) In the given sum there are 5 consecutive odd numbers.

Therefore,

$n =5$

$n^2 = 5^2 =25$.

(ii)  In the given sum there are 10 consecutive odd numbers.

Therefore,

$n =10$

$n^2 = 10^2 =100$.

(iii)  In the given sum there are 12 consecutive odd numbers.

Therefore,

$n =12$

$n^2 = 12^2 =144$.

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Updated on: 10-Oct-2022

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