Be observing the table, we can write the following conjecture:
When adding consecutive even numbers, starting from 2 to [tex]m[/tex].
Then the sum is equal to:
[tex] \frac{m}{2}( \frac{m}{2} +1) [/tex]
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 [tex]m=30[/tex]:
[tex]\frac{m}{2}( \frac{m}{2} +1)=\frac{30}{2}( \frac{30}{2} +1)=(15)(16)=240[/tex]
The answer is 240.
