Question

find the sum of first 100 even natural numbers​

Answer 1

Step-by-step explanation:

Ap = 2,4,6,8

a= 2

n=100

d= 2

an=?

an = a+ (n-1) d

an= 2 + (100-1)×2

an = 2+ 99×2

an= 2+ 198

an = 200

sum of first 100 even terms

sn = n/2 ( a + an)

sn = 100/2( 2+200)

sn= 50 ( 202)

S100 = 10100

Answer 2

Answer:

The sum of the first 100 even natural numbers​ is 10100

Step-by-step explanation:

We have to find the sum of the first 100 even numbers.

So,

The formula is used to determine such a given series.

Formula:- $\dfrac{n(n+2)}{4}$

where,

• n - represents the last number in the series which is 200.

• In other series, the 2 would be equal to the amount between each pair of numbers, and the 4 would be twice the amount.

To solve, substitute the values in the given formula:

$\dfrac{n(n+2)}{4}$

= $\dfrac{200(200+2)}{4}$

= $\dfrac{200(202)}{4}$

= $\dfrac{40400}{4}$

= 10100

Therefore, the sum of the first 100 even numbers is 10100.