Question

The mean of first 673 natural numbers is _________.

Answer 1

The first 673 natural numbers are 1, 2, 3, ..., 673.

These are in AP with a = 1, l = 673 and n = 673.

∴ Sum of first 673 natural numbers

$$\begin{gathered} =1+2+3+...+673 \\ =\frac{673}{2}\left(1+673\right)\left[S_n=\frac{n}{2}\left(a+l\right)\right] \\ =\frac{673}{2}\times 674 \\ =673\times 337 \end{gathered}$$

Now,

Mean of first 673 natural numbers $=\frac{\mathrm{Sum}\mathrm{of}\mathrm{first}673\mathrm{natural}\mathrm{numbers}}{673}=\frac{673\times 337}{673}=337$

The mean of first 673 natural numbers is ___337___.