Which term of the AP 2, 11, 20, 29, ..... is
290:

To find which term of the arithmetic progression (AP) is 290, we need to use the formula for the \( n \)-th term of an AP:

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

Where:
- \( a_n \) is the \( n \)-th term.
- \( a_1 \) is the first term.
- \( d \) is the common difference.
- \( n \) is the term number.

Given:
- \( a_1 = 2 \)
- \( d = 11 - 2 = 9 \)
- \( a_n = 290 \)

We substitute the values into the formula:

\[
290 = 2 + (n - 1) \cdot 9
\]

Subtract 2 from both sides:

\[
288 = (n - 1) \cdot 9
\]

Divide by 9:

\[
n - 1 = \frac{288}{9} = 32
\]

Add 1 to both sides:

\[
n = 33
\]

Therefore, the 33rd term of the AP is 290.

Would you like more details or have any questions about this solution?

Here are 5 related questions:
1. What is the sum of the first 33 terms of this AP?
2. How many terms of this AP are less than 1000?
3. If 290 is the 33rd term, what is the 50th term?
4. How would the AP change if the common difference were doubled?
5. Find the difference between the 10th and 20th terms of this AP.

**Tip:** Understanding the formula for the \( n \)-th term in an AP is crucial for identifying specific terms and solving related problems quickly.

Learn how to find the specific term of an arithmetic progression (AP) where the sequence starts at 2 and increases by 9 each step until it reaches 290. Detailed step-by-step solution using the formula for the n-th term of an AP. Suitable for Grades 7-9 students studying arithmetic sequences.

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