Use inductive reasoning and make a conjecture about each value?

Question

Use inductive reasoning and make a conjecture about each value?

The sum of the first 30 positive even numbers and if that means to add 30 of the first positive numbers then it comes out to 930. But then it says to find one couterexample to show that the conjecture is false. STUPID GEOMETRY i don't get this can you please help?

Answer 1

15*16

Answer 2

The possibilities are endless. Try this one:

Conjecture:

The sum of the first N consecutive even numbers is divisible by N.

Example: N = 0 → 2 + 4 + .... + 60 = 930 = 31×30

Example: N = 7 → 2 + 4 + 6 + 8 + 10 +12 + 14 = 56 = 8×7

That one's true so that's not helpful. I don't know why they have you conjecturing things that might be true... how do you find a counterexample for things that are true?

How about this:

The sum of the first N consecutive even numbers ends in 0.

That's false (look at the examples above for one that works - 930 - and one that doesn't - 56).