Question 699438
When dealing with consecutive integers (or consecutive odd integers, or consecutive even integers),
you name one of them as your variable,
and write the other(s) number(s) as a function of the one you named.
Two consecutive integers could be named {{{n}}} and {{{(n+1)}}}.
Some strategies to name your integers seem to work better than others.
 
Three consecutive integers can be called {{{(n-1)}}}, {{{n}}}, and {{{(n+1)}}}.
Their sum would be {{{3n}}}.
If that sum is {{{66}}, then
{{{3n=66}}} --> {{{n=66/3}}} --> {{{highlight(n=22)}}}
The three numbers are {{{21}}}, {{{22}}}, and {{{23}}}.
 
Three consecutive odd integers (or three consecutive even integers) can be called
{{{(n-2)}}}, {{{n}}} and {{{(n+2)}}} ,
because consecutive odd integers are 2 units apart (and so are consecutive even integers).
The sum of the three consecutive odd integers {{{(n-2)}}}, {{{n}}} and {{{(n+2)}}}
is also {{{3n}}}.
If that sum is {{{51}}} , then
{{{3n=51}}} --> {{{n=51/3}}} --> {{{highlight(n=17)}}}
The three numbers are {{{15}}}, {{{17}}}, and {{{19}}}.
 
NOTES: You could give your numbers different names.
I've tried other options before,
but I think my current choices work best.
Consecutive integers, consecutive odd integers, and consecutive even integers
are numbers in arithmetic sequence.
If you learned about arithmetic sequences,
you might remember that their median is their average.
The average of 3, or 5, or 7 (or any odd quantity of such numbers) is the number in the middle.
The sum is the average times the "quantity of such numbers".