Find the 91st term of the arithmetic sequence 28, comma, 8, comma, minus, 12, comma, point, point, .28,8,−12,

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!

Find the 91st term of the arithmetic sequence 28, 8, -12, ...

Learn how to find the 91st term of an arithmetic sequence with first term 28 and common difference -20. Follow a step-by-step guide to use the n-th term formula for arithmetic sequences. Suitable for students in Grades 8-10.

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