Answer:
15, 11, 7, 3, -1, -5, -9, -13
Step-by-step explanation:
Inserting Arithmetic Means (AM's)
Suppose we want to insert n equally-spaced numbers inside a given interval with endpoints [x,y].
To place n numbers, we need to open n+1 spaces, at the end of which, a new number will be placed. The given interval is then divided into n+1 rational numbers of a value (y-x)/(n+1).
We need to insert 6 AM's between 15 and -13. Each AM will be inserted at a space of (-13-15)(6+1)=-28/7=-4.
Thus the sequence is formed subtracting 4:
15
15-4=11
11-4=7
7-4=3
3-4=-1
-1-4=-5
-5-4=-9
-9-4=-13
The sequence is (numbers in bold are the AM's):
15, 11, 7, 3, -1, -5, -9, -13
