Find the sum of the arithmetic sequence 22, 11, 0, −11, …, −77.
	A.	−198
	B.	−275
	C.	−297
	D.	−385

We are given an arithmetic sequence: 22, 11, 0, −11, …, −77, and asked to find the sum of the terms.

### Step 1: Identify the necessary parameters

1. **First term (a)**: The first term is 22.
2. **Common difference (d)**: The difference between consecutive terms is:
   \[
   d = 11 - 22 = -11
   \]
3. **Last term (l)**: The last term given is −77.

### Step 2: Find the number of terms (n)

The formula for the \(n\)-th term of an arithmetic sequence is:
\[
a_n = a + (n - 1) \cdot d
\]
We know that \(a_n = -77\), \(a = 22\), and \(d = -11\). Substituting these values into the formula:
\[
-77 = 22 + (n - 1) \cdot (-11)
\]
Simplifying:
\[
-77 = 22 - 11(n - 1)
\]
\[
-77 - 22 = -11(n - 1)
\]
\[
-99 = -11(n - 1)
\]
Dividing both sides by -11:
\[
n - 1 = 9
\]
\[
n = 10
\]
So, there are 10 terms in the sequence.

### Step 3: Use the sum formula for an arithmetic sequence

The sum of the first \(n\) terms of an arithmetic sequence is given by the formula:
\[
S_n = \frac{n}{2} \cdot (a + l)
\]
Substituting \(n = 10\), \(a = 22\), and \(l = -77\):
\[
S_{10} = \frac{10}{2} \cdot (22 + (-77)) = 5 \cdot (22 - 77) = 5 \cdot (-55) = -275
\]

Thus, the sum of the sequence is \( \boxed{-275} \).

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Do you want more details or have any other questions?

Here are some related questions for practice:
1. Find the sum of the arithmetic sequence with first term 15, common difference -5, and last term -25.
2. What is the sum of the first 20 terms of the arithmetic sequence where \(a = 7\) and \(d = 3\)?
3. How many terms are there in the arithmetic sequence 10, 7, 4, ..., -50?
4. Find the sum of the arithmetic sequence: 3, 8, 13, ..., 98.
5. Determine the common difference of an arithmetic sequence if the first term is 6 and the 10th term is -18.

**Tip**: Always check the number of terms in an arithmetic sequence before applying the sum formula!

Find the sum of the arithmetic sequence 22, 11, 0, −11, …, −77.
A. −198
B. −275
C. −297
D. −385

Learn how to find the sum of the arithmetic sequence 22, 11, 0, −11, …, −77. This detailed solution covers key concepts such as the arithmetic sequence formula, common difference, and number of terms. Suitable for students in Grades 9-12.

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