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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

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An Intiative by Sri Chaitanya

25, 100 and 144

20, 80 and 99

35, 30 and 33

45, 40 and 44

answer is A.

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Detailed Solution

In the first part we have,
1+3+5+7+9
These are first consecutive odd terms. Now we know that the sum of first n consecutive n terms =

= n^{2}

So, the sum of these 5 first consecutive odd terms,

= 5^{2}

= 25

Now, in the second part we have,
1+3+5+7+9+11+13+15+17+19
So, the sum of these 10 first consecutive odd terms,

= 10^{2}

= 100

In the third part we have,
1+3+5+7+9+11+13+15+17+19+21+23
So, the sum of these 12 first consecutive odd terms,

= 12^{2}

= 144

So, the required sum is 25, 100 and 144.
Option 1 is correct.

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