We are to fill the 6 blanks below so that the sequence

12, __, __, __, __, __, __, __, 75

of 8 terms is an arithmetic sequence. We use
the formula:



using a1=12, n=8, a8=75



 









So we add 9 six times, starting by adding it
to 12, and the 6 arithmetic means are the 6
underlined numbers below:

12, 21, 30, 39, 48, 57, 66, 75

and as a check, when we add 9 to the last one, 66, we do get 75.

Edwin