Question

find the sum of all the even numbers between 200 to 500

Answer 1

Answer:

Step-by-step explanation:

The even no start from 202;204......;498.

Sn equal to n/2(a+an)

n eqls to an- a/d +1

498-202/2+1 equal to 189

Sn eql to 189/2(202+498) e 66150

Answer 2

The sum of all the even numbers between 200 to 500 is 52150.

Step-by-step explanation:

Consider the provided information.

We need to find the sum of all the even numbers between 200 to 500.

The first even number between 200 to 500 is 202 and the last even number between 200 and 500 is 498.

As we know that we can find the next even number by adding 2 to the previous even number.

Thus, the required series is: 202, 204, 206,......,498

Now find the total number of terms in the above A.P by using the formula:

$a_n=a+(n-1)d$

Substitute a = 202, d = 2 and aₙ = 498 in above formula.

$498=202+(n-1)2$

$296=(n-1)2$

$148=n-1$

$n=149$

Hence, there are total 149 terms.

To calculate the sum, use the formula: $s_n=\dfrac{n}{2} (a+l)$

$s_n=\dfrac{149}{2} (202+498)$

$s_n=\dfrac{149}{2} (700)$

$s_n=149\times 350$

$s_n=52150$

Hence, the sum of all the even numbers between 200 to 500 is 52150.

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