Find 4 arithmetic means between -5 and 15.

Explanation

To find 4 arithmetic means between -5 and 15, we can follow these steps:

### Step 1: Identify the values
We have:
- First term (a) = -5
- Last term (b) = 15
- Number of arithmetic means (n) = 4

### Step 2: Calculate the common difference (d)
The formula for the common difference when there are n arithmetic means between two numbers a and b is given by:

\[ d = \frac{b - a}{n + 1} \]

Substituting the values we have:

\[ d = \frac{15 - (-5)}{4 + 1} = \frac{15 + 5}{5} = \frac{20}{5} = 4 \]

### Step 3: Find the arithmetic means
Now that we have the common difference (d = 4), we can find the arithmetic means. The arithmetic means can be expressed as follows:

- First arithmetic mean (A1) = a + d = -5 + 4 = -1
- Second arithmetic mean (A2) = a + 2d = -5 + 2(4) = -5 + 8 = 3
- Third arithmetic mean (A3) = a + 3d = -5 + 3(4) = -5 + 12 = 7
- Fourth arithmetic mean (A4) = a + 4d = -5 + 4(4) = -5 + 16 = 11

### Step 4: List the arithmetic means
The four arithmetic means between -5 and 15 are:
- A1 = -1
- A2 = 3
- A3 = 7
- A4 = 11

### Final Answer:
The four arithmetic means between -5 and 15 are -1, 3, 7, and 11.

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