To find the arithmetic mean of the sequence 10, ___, ___, ___, -18, we need to fill in the missing values first.
Since the sequence has five terms, and the first and last terms are given, we can use the formula for the arithmetic mean to find the missing terms:
arithmetic mean = (sum of terms) / (number of terms)
We know that the sum of the terms is equal to:
10 + x + y + z - 18
Simplifying:
x + y + z - 8
Since there are five terms in the sequence, we can set the arithmetic mean equal to:
(arithmetic mean) = (10 + x + y + z - 18) / 5
Simplifying:
(arithmetic mean) = (x + y + z - 8) / 5
We can now substitute the given arithmetic mean into the equation and solve for x + y + z:
-5 = (x + y + z - 8) / 5
Multiplying both sides by 5:
-25 = x + y + z - 8
Simplifying:
x + y + z = -17
Now that we know the sum of the terms, we can find the arithmetic mean by dividing by the number of terms:
(arithmetic mean) = (10 + x + y + z - 18) / 5
(arithmetic mean) = (-17 + 10 + (-18) - 18) / 5
(arithmetic mean) = -43 / 5
(arithmetic mean) = -8.6
Therefore, the arithmetic mean of the sequence 10, ___, ___, ___, -18 is -8.6.