To find the common difference $d$ in an arithmetic sequence, we can use the formula for the $n$-th term of the sequence:

$a_n = a_1 + (n-1) \cdot d$

Here:

• $a_1 = 8$ (the first term)
• $a_6 = 3$ (the sixth term)
• $n = 6$

Substitute these values into the formula for $a_n$:

$a_6 = a_1 + (6-1) \cdot d$

$3 = 8 + 5d$

Now, solve for $d$:

$3 - 8 = 5d$

$-5 = 5d$

$d = \frac{-5}{5} = -1$

So, the common difference $d$ is $-1$.

Would you like more details or have any questions?

Here are 5 related questions:

1. How do you find the $n$-th term of an arithmetic sequence given $a_1$ and $d$?
2. What is the sum of the first 10 terms of this arithmetic sequence?
3. If the common difference was positive, what would $a_6$ be?
4. How would the sequence change if the first term were negative?
5. What is the general formula for the sum of an arithmetic sequence?

Tip: In arithmetic sequences, the difference between consecutive terms is always constant, which makes it easy to identify patterns or missing terms.