Question

Find the sum.
10 + 12 + 14 + ... + 80

Answer 1

1620

Explanation:

The amount of even integers between 10 and 80 inclusive is 36 (5 for each interval of 10 [e.g., 10-19 has 5, 20-29 has 5] and one extra for 80).

Since the numbers are consecutive even numbers, we can use the fact that the sum of the numbers is equal to the average of the numbers, times the number of numbers.

The average of the numbers is 45, since
`(10+80)/(2)=45`. We can use only the two outer numbers to determine the average since the numbers are all evenly spaced as they are consecutive even numbers.

`45*36=1620`, so the sum is 1620.