Question

what is the sum of the even integers from 100 to 1000

Answer 1

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Here is your answer

Answer 2

Answer:

The sum of even integers from 100 to 1000 is 248050

Step-by-step explanation:

The even integers from 100 to 1000 are :

100, 102, 104, ..........1000

The above terms are in A.P. with first term, a = 100 and common difference, d = 2

Now, last term = a + (n - 1)d

⇒ 1000 = 100 + (n - 1)2

⇒ 900 = (n - 1)2

⇒ n - 1 = 450

⇒ n = 451

Now, Sum is given by :

$Sum = \frac{n}{2}\times(a+l)\\\\\implies Sum =\frac{451}{2}\times(100+ 1000)\\\\ \implies Sum=\frac{451}{2}\times 1100\\\\\implies Sum = 248050$

Hence, The sum of even integers from 100 to 1000 is 248050