Question

Look at the table. Make a conjecture about the sum of the first 10 positive even numbers.

Answer 1

The answer is 10•11, if you look at the pattern, you don't have to solve the addition.

Answer 2

The sum of the first 10 positive even numbers is
`10* 11=110`

Explanation:

From the table, we see that,

Sum of the numbers
`2+4+6+8+10=30=5* 6=5(5+1)`

That is, when there are 5 terms in the sequence, the sum is given by
`5* 6`.

Then, in general, when there are 'n' terms in the sequence, the sum is given by
`n(n+1)`

We are required to find the sum of 10 even terms.

Therefore, when there are 10 terms in the sequence, the sum will be
`10(10+1)=10* 11`

Hence, the sum of the first 10 positive even numbers is
`10* 11=110`