The sum of the first 15 positive even numbers is 240. (Simply square 15, then add 15 to the result: 15 x 15 = 225. 225 + 15 = 240).
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There is no conjecture about the sum of the first 30 positive even numbers. The answer can be derived and proven. A statement that has been proven is no longer a conjecture.
The answer to what is the sum of the first positive even numbers is 930. It doesn't mean that you add all the even numbers up until you reach the number 30. In fact, since you have to get the sum of the even numbers, you have to add all even numbers until you get to the number 60.
You do not need a conjecture; you can calculate the answer. The answer is 10,100
The first ten positive numbers total 55.
The sum of the first 50 even numbers is 2,550.