Question 1091303
<pre>
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:

{{{a[n]}}}{{{""=""}}}{{{a[1]+(n-1)d}}}

using a<sub>1</sub>=12, n=8, a<sub>8</sub>=75

{{{a[8]}}}{{{""=""}}}{{{12+(8-1)d}}}

{{{75}}}{{{""=""}}}{{{12+(8-1)d}}} 

{{{75}}}{{{""=""}}}{{{12+7d}}}

{{{63}}}{{{""=""}}}{{{7d}}}

{{{63/7}}}{{{""=""}}}{{{7d/7}}}

{{{9}}}{{{""=""}}}{{{d}}}

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

12, <u>21</u>, <u>30</u>, <u>39</u>, <u>48</u>, <u>57</u>, <u>66</u>, 75

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

Edwin</pre>