To find the 91st term of the arithmetic sequence, we need to identify the first term ($a$) and the common difference ($d$) of the sequence.

Step 1: Identify the First Term and Common Difference

The first term ($a$) is the first number in the sequence: $a = 28$

The common difference ($d$) is the difference between consecutive terms: $d = 8 - 28 = -20$

So, the common difference is $-20$.

Step 2: Use the Formula for the $n$-th Term of an Arithmetic Sequence

The formula for the $n$-th term ($a_n$) of an arithmetic sequence is: $a_n = a + (n - 1) \cdot d$

To find the 91st term, set $n = 91$:

$a_{91} = 28 + (91 - 1) \cdot (-20)$

Step 3: Calculate the 91st Term

Now, substitute the values:

$a_{91} = 28 + 90 \cdot (-20)$

$a_{91} = 28 - 1800$

$a_{91} = -1772$

Conclusion

The 91st term of the arithmetic sequence is: $\boxed{-1772}$

Would you like to know more details or have any questions?

Relative Questions:

1. What is the formula for the sum of the first $n$ terms of an arithmetic sequence?
2. How can we find the number of terms in a finite arithmetic sequence?
3. How does changing the common difference affect the arithmetic sequence?
4. Can an arithmetic sequence have a common difference of zero?
5. How do we find the $n$-th term if given any two terms of an arithmetic sequence?

Tip:

When working with arithmetic sequences, remember that the common difference can be negative, indicating that the sequence is decreasing!