Question

Find the sum of the AP: $2,4,6,...$ upto $100$ terms.

Answer 1

Find the sum of the AP up to $100$ terms:

We know that the sum of first $n$ terms of an AP is

$S_n=\frac{n}{2}[2a+(n-1\left)d\right]$

Where $a=$ first term and $d=$ common difference

We have, AP: $2,4,6,...$ upto$100$ terms

Here, first term $a=2.$

Common difference $d=4-2=2$ and $n=100$.

$\begin{array}{rcl}& \Rightarrow & S_{100}=\frac{100}{2}[2\times 2+(100-1)\times 2]\\ & =& 50[4+99\times 2]\\ & =& 50[4+198]\\ & =& 50\times 202\\ & =& 10100\end{array}$

Hence, the required answer is $10100$.