Question

Look at the table. Make a conjecture about the sum of the first 15 positive even numbers.

Answer 1

Be observing the table, we can write the following conjecture:

When adding consecutive even numbers, starting from 2 to $m$.

Then the sum is equal to: 
$\frac{m}{2}( \frac{m}{2} +1)$

Then, the sum of the first 15 positive even numbers (which is the sum of 2 to 30) can be calculated with the previous conjecture by setting $m=30$:
$\frac{m}{2}( \frac{m}{2} +1)=\frac{30}{2}( \frac{30}{2} +1)=(15)(16)=240$

The answer is 240.