Question

How many even numbers are there between $1$ to $100$?

Answer 1

Step 1: Establish the series

Numbers that are divisible by $2$ are called even numbers.

The given range is $1$ to $100$.

Hence, the series can be written as,

$2,4,6,8,10......,90,92,94,96,98$

As we can see it forms an AP series.

Step 2: Calculate the number of even numbers

Here we have,

The first term $a_1=2$

The $n^{th}$ term $a_n=98$

The common difference $d=2$

If $n$ is the number of terms, we get

$\therefore a_n=a_1+\left(n-1\right)d$

$\Rightarrow 98=2+\left(n-1\right)2$

$\Rightarrow 49=1+n-1$

$\therefore n=49$

Hence, there are $49$ even numbers between $1$ to $100$.