Pearl writes down seven consecutive integers, and adds them up. The sum of the integers is equal to 21*4 times the largest of the seven integers. What is the smallest integer that Pearl wrote down?

So for your question , there are seven integers which we can put it like this:

n + n+1 n+2 ....... n+6,which will equal

7n + 21 which makes

6 * (n+6) = 6n+36

7n+21 = 6n+36

n = 15

15 is the smallest number for your problem :)

Please excuse my ignorance; I'm trying to learn.

Where did the 6 come from in " 6 * (n+6) = 6n+36 " ?

6 is the 6th number in the sequence