Question

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

Answer 1

The conjecture about the sum of the first 15 positive even numbers is 15 * 16

Making a conjecture about the sum of the first 15 positive even numbers.

From the question, we have the following parameters that can be used in our computation:

The table of values

Where, we have

2 = 1 * 2

2 + 4 = 2 * 3

2 + 4 + 6 = 3 * 4

And so on

This means that

Sum of first n positive even numbers = n * (n + 1)

So, for the first positive even numbers, we have

n = 15

This gives

Sum of first 15 positive even numbers = 15 * (15 + 1)

Evaluate

Sum = 15 * 16

Sum = 240

Hence, the sum is 15 * 16

Answer 2

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:

`(m)/(2)( (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`:

`(m)/(2)( (m)/(2) +1)=(30)/(2)( (30)/(2) +1)=(15)(16)=240`

The answer is 240.