Question

Find the sum of AP: 2,4,6,__, 100 terms​

Answer 1

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Answer 2

Answer:

The sum of first hundred terms of the given AP is $10100$ .

Step-by-step explanation:

AP , Arithmetic Progression is a sequence of numbers which either increases or decreases by a fixed number. This fixed number is called the common difference, denoted by d , it can be positive, negative or zero.

In this question we are asked to find the sum of first hundred terms of the AP :

$2,4,6, . . .$

We have the formula for finding the sum of first n terms of an AP as :

$S_{n} = \frac{n}{2} [2a+(n-1)d]$ , where $a$ is the first term

                                      $d$ is the common difference

                                   and $n$ number of terms to be added.

Here   $a=2,\ d=2,\ n=100$ .

Therefore     $S_{100} =\frac{100}{2} [2*2+99*2]$

                            $=50[4+198]\\\\=50*202\\\\=10100$.

Hence the answer.

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