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The problem in the image states:

"In an arithmetic sequence with \( a_1 = -18 \) and \( d = 9 \), which term is 63?"

To solve this, we can use the formula for the \(n\)-th term of an arithmetic sequence:

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

Where:
- \( a_n \) is the \(n\)-th term,
- \( a_1 \) is the first term of the sequence,
- \( d \) is the common difference between consecutive terms,
- \( n \) is the position of the term we are looking for.

Given:
- \( a_1 = -18 \),
- \( d = 9 \),
- \( a_n = 63 \).

We substitute these values into the equation and solve for \(n\):

\[
63 = -18 + (n-1) \cdot 9
\]

Let me solve this equation.The term 63 is the 10th term of the arithmetic sequence.

Would you like further details or have any other questions? Here are 5 related questions for practice:

1. What is the formula for the sum of the first \( n \) terms of an arithmetic sequence?
2. How do you determine the first term if the 10th term and the common difference are given?
3. If the common difference were negative, how would the sequence behave?
4. Can you find the 20th term of this arithmetic sequence?
5. What is the general form of an arithmetic sequence?

**Tip:** Always double-check the formula and ensure correct substitution of values when solving sequence problems.

In an arithmetic sequence with a1 = -18 and d = 9, which term is 63?

Learn how to determine which term of an arithmetic sequence equals 63. This example uses a first term of -18 and a common difference of 9, applying the formula for arithmetic sequences. Suitable for students in Grades 9-10.

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