Question

Prathyusha stated that "the average of first $10$ odd numbers is also $10$". Do you agree with her? Justify your answer.

Answer 1

First $10$ odd numbers-

$1,3,5,7,9,11,13,15,17,19$

The above series forms an A.P. with first term and common difference of $1$ and $2$.

As we know that sum of $n$ terms in an A.P. is given as-

$S_n=\frac{n}{2}(a+l)$

Whereas, $a$ and $l$ are first and last term.

Sum of first $10$ odd numbers-

$\therefore S_{10}=\frac{10}{2}(1+19)$

$\Rightarrow S_{10}=5\times 20=100$

Now, average of first $10$ odd numbers-

Av. $=\frac{S_n}{n}=\frac{100}{10}=10$

Thus the average of first $10$ odd numbers is $10$.

Hence I agree with Pratyusha as the average of first $10$ odd numbers is $10$.