Name: Patterns of Square Numbers
Uploaded: 2019-07-19
Duration: 9 min 26 s
Description: Did you know that square numbers form various patterns? The square of any odd natural number apart from 1 can be expressed as the sum of two consecutive natu...

Question

Lalit has some chocolates. He distributed these chocolates among

13

children in such a way that he gave one chocolate to first child,

3

chocolates to second child,

5

chocolates to third and so on. Find the number of chocolates Lalit had.

Accepted Answer

Number of children $= 13$

It is given that Lalit has given chocolates to the children in such a way that the number of chocolates to first child is $1$ , the number of chocolates to the second child is $3$ , the number of chocolates to the third child is $5$ and so on.

Let us write the pattern of number of chocolates given to the children as $1, 3, 5$ , .... which are the consecutive odd numbers starting from $1$ .

In order to find the total number of chocolates he distributed to the children, we need to consider the sum of the first $13$ consecutive odd numbers starting from $1$ , i.e. $1 + 3 + 5 + 7 + 9 + 11 + 13 + 15 + 17 + 19 + 21 + 23 + 25$ .

We know that sum of the first $n$ odd numbers starting from $1$ is $n^{2}$ .

So, $1 + 3 + 5 + 7 + . . . . . . . . . (up to 13 terms) = 13^{2} = 13 \times 13 = 169$

Hence, Lalit had $169$ chocolates.

Lalit has some chocolates. He distributed these chocolates among $13$ children in such a way that he gave one chocolate to first child, $3$ chocolates to second child, $5$ chocolates to third and so on. Find the number of chocolates Lalit had.

Important Questions on Squares and Square Roots

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