The sum of first 50 even numbers is 2550 .What is the sum of even numbers from 102 to 200 inclusive?

1)5100
2)7550
3)10100
4)15500
5)20100

Please also suggest on with below question :

The sum of first 50 even numbers is 650 [using Formula :m/2 (m/2+1)] ,why is it 2550 ?

The answer is 7550.
"The sum of first 50 even numbers is 2550" ---- means that 1 to 100 numbers, there are 50 even numbers (ex; 2,4,6,8,10,......92,94,96,98,100). if you add 2+4+6+8+........98+100 (the even numbers), the answer will be 2550. The second part: "What is the sum of even numbers from 102 to 200 inclusive?" we knew that for first 50 even number is 2550, then think about that: 102 is 100 more than 2, 104 is 100 more than 4, 106 is 100 more than 6,... 198 is 100 more than 98, and 200 is 100 more than 100. so, 102+104+106+108+110=530 which is 500 more than 30 (2+4+6...+10), 112+114+.....+120 it will also 500 more than 80 (12+14+....+20). Thus, 122+124+....130 will also be 500 more than 22+24+....+30, then you add those 500 all together (in fact there are 10 of 500 number, start from 102+....110, 112+....+120, 122+...+130,......190+....+200), you will have 5000.

Remember the sum of first 50 even numbers is 2550 than you add 5000 to it , now the winner is 7550 :)

thank you!

that's the first time i've ever seen a formula for that.

you aren't using the formula correctly; the way it's written, "m" must stand for the greatest number out of your list of even numbers, NOT the number of terms in the sequence.
therefore, "m" is 100, and so your formula gives (50)(50 + 1) = 2550, as expected.

here's a compact presentation:

102 + 104 + 106 + ... + 200
=
(100 + 2) + (100 + 4) + (100 + 6) + ... + (100 + 100)
=
(100 + 100 + 100 + ... + 100) + (2 + 4 + 6 + ... + 100)
=
(fifty 100's) + (2550 as given)
=
5000 + 2550
=
7550