What is the average of the first 50 positive even numbers?

The first positive even number is 2 and the 50th positive even number will be 100.

So the series will be 2, 4, 6, 8 ............... 100.

Sum of the above-given series = $$\frac{n}{2}\times\ \left[2a+\left(n-1\right)d\right]$$

n = number of terms = 50

a = first term = 2

d = difference in the consecutive terms = 2

Put all the values in the formula.

Sum = $$\frac{50}{2}\times\ \left[2\times2+\left(50-1\right)2\right]$$

= $$25\times\ \left[4+49\times\ 2\right]$$

= $$25\times\ \left[4+98\right]$$

= $$25\times\ 102$$

average of the first 50 positive even numbers = $$\frac{25\times\ 102}{50}$$

= $$\frac{102}{2}$$

= 51

Shortcut::

average of the first 50 positive even numbers = $$\frac{first\ term\ +last\ term}{2}$$

= $$\frac{2\ +100}{2}$$

= $$\frac{102}{2}$$

= 51