Question

There are 20 consecutive even numbers. how much bigger is the sum of the 10 larger ones than the sum of the ten smaller ones?

Answer 1

200

Explanation:

:)

Answer 2

Let the numbers be:

`2n,2(n+1),...,2(n+19)\\\text{Sum of the 10 biggest ones:}\\2(n+10)+...+2(n+19)=2((n+10)+...+(n+19))\\=2*10(n+10+n+19)/(2)\\=10(2n+29)\text{the sum of an arithmetic sequence}`
The sum of the ten smaller one in the same manner:

`2(n)+...+2(n+9)=2(n+...+(n+9))\\=2*10(n+n+9)/(2)`
Compute the difference of the above two sums:

`\\10(2n+29)-10\(2n+9)=290-90=200`

The bigger sum is 200 more bigger than the sum o the ten smaller sum.