The sum is always five times greater than what number?
Conjecture: The sum of any five consecutive integers is five times the third number.
Practice makes perfect
Let's attempt to find a pattern by calculating the sum of some arbitrary consecutive integers. Notice that consecutive integers means they follow each other.
1+2+3+4+5&=15
3+4+5+6+7&=25
6+7+8+9+10&=40
9+10+11+12+13&=55Examining the sums, we see that all of them equal an integer that is five times greater than the sequence third number. With this information we can write a conjecture.
Conjecture
The sum of any five consecutive integers
is five times the third number.
Let's test this a few times with some other integers.
2+3+4+5+6&=20
5+6+7+8+9&=35
8+9+10+11+12&=50
10+11+12+13+14&=60
It would appear that our conjecture is true.
