Question 332361
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The other tutor's solution is incorrect.  He only inserted 
one arithmetic mean.

Find two arithmetic means between -17 and -71.

-17, ___, ___, -71

So the first term, a<sub>1</sub> is -17 and the 4th term a<sub>4</sub> is -71.

a<sub>n</sub> = a<sub>1</sub> + (n - 1)d

We substitute n=4, 

a<sub>4</sub> = a<sub>1</sub> + (4 - 1)d
a<sub>4</sub> = a<sub>1</sub> + 3d

We substitute a<sub>1</sub>=-17 and a<sub>4</sub>=-71

-71 = -17 + 3d

Solve for d

-54 = 3d
-18 = d

-17, ___, ___, -71

To fill in the first blank -17+(-18) = -35  

-17, -35, ___, -71

To fill in the second blank -35+(-18) = -53

-17, -35, -53, -71

That's it.  But as a check let's add -18 to -53.
Yes, we get (-53)+(-18) = -71.

So the two arithmetic means are -35 and -53.

Edwin</pre>