Find 6 arithmetic means between 8 and 29.

Explanation

To find 6 arithmetic means between 8 and 29, we can follow these steps:

### Step 1: Identify the values
Let:
- \( a = 8 \) (the first term)
- \( b = 29 \) (the last term)
- \( n = 6 \) (the number of arithmetic means)

### Step 2: Calculate the common difference
The formula for the common difference \( d \) 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:

\[ d = \frac{29 - 8}{6 + 1} = \frac{21}{7} = 3 \]

### Step 3: Find the arithmetic means
The arithmetic means can be expressed as follows:
- The first arithmetic mean \( a_1 = a + d \)
- The second arithmetic mean \( a_2 = a + 2d \)
- The third arithmetic mean \( a_3 = a + 3d \)
- The fourth arithmetic mean \( a_4 = a + 4d \)
- The fifth arithmetic mean \( a_5 = a + 5d \)
- The sixth arithmetic mean \( a_6 = a + 6d \)

Now, we can calculate each arithmetic mean:

1. \( a_1 = 8 + 1 \times 3 = 8 + 3 = 11 \)
2. \( a_2 = 8 + 2 \times 3 = 8 + 6 = 14 \)
3. \( a_3 = 8 + 3 \times 3 = 8 + 9 = 17 \)
4. \( a_4 = 8 + 4 \times 3 = 8 + 12 = 20 \)
5. \( a_5 = 8 + 5 \times 3 = 8 + 15 = 23 \)
6. \( a_6 = 8 + 6 \times 3 = 8 + 18 = 26 \)

### Step 4: List the arithmetic means
The 6 arithmetic means between 8 and 29 are:

\[ 11, 14, 17, 20, 23, 26 \]

### Final Answer:
The 6 arithmetic means between 8 and 29 are **11, 14, 17, 20, 23, and 26**.

---