answer :
{16, 18, 20, 22, 24}
other answers :
{17, 18, 20, 22, 23}
{14, 16, 20, 24, 26}
{10, 14, 20, 26, 30}
{18, 18, 20, 22, 22} (if repetition is allowed)
explanation:
To come up with sets of numbers that satisfy the given conditions, we can use algebra and solve for the unknowns.
Let x be the smallest number in the set. Then, the other numbers in the set must be x + a, x + 2a, x + 3a, and x + 4a, where a is the common difference between consecutive terms.
We can use the formula for the mean of a set of numbers to get:
(5x + 10a) / 5 = 20
Simplifying this equation, we get:
x + 2a = 20
Now, we need to find a set of values for x and a such that the range (i.e., the difference between the largest and smallest numbers in the set) is 8. This gives us another equation:
(x + 4a) - x = 8
Simplifying this equation, we get:
4a = 8
a = 2
Substituting this value of a into the equation x + 2a = 20, we get:
x + 4 = 20
x = 16
So, we know that the smallest number in the set must be 16 and the common difference between consecutive terms must be 2. Using this information, we can construct sets of numbers that satisfy the given conditions, such as the ones I provided earlier.
Mean 20, Range 8.
Sure, one possible set of numbers that satisfy the given conditions is:
{16, 18, 20, 22, 24}
To check:
The mean of these numbers is (16 + 18 + 20 + 22 + 24) / 5 = 20.
The range of these numbers is the difference between the largest and smallest numbers, which is 24 - 16 = 8.
Here are some other possible sets of numbers that also satisfy the conditions:
{17, 18, 20, 22, 23}
{14, 16, 20, 24, 26}
{10, 14, 20, 26, 30}
{18, 18, 20, 22, 22} (if repetition is allowed)
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