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

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

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

where:
- \(a_n\) is the \(n\)th term,
- \(a\) is the first term,
- \(d\) is the common difference,
- \(n\) is the term number we need to find.

Given:
- The first term \(a = 2\),
- The common difference \(d = 11 - 2 = 9\),
- \(a_n = 290\).

Substitute these values into the formula:

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

Now, solve for \(n\):

\[
290 = 2 + 9(n - 1)
\]
\[
290 - 2 = 9(n - 1)
\]
\[
288 = 9(n - 1)
\]
\[
n - 1 = \frac{288}{9}
\]
\[
n - 1 = 32
\]
\[
n = 33
\]

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

Would you like more details or have any other questions?

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Here are some related questions you might find interesting:

1. What is the sum of the first 33 terms of this AP?
2. How would you find the common difference if only the first and last terms were given?
3. What is the 50th term of the given AP?
4. How can you find the middle term in an AP sequence?
5. How do you determine if a given number is a term in a given AP?

**Tip:** Always check that the common difference is consistent throughout the sequence when working with arithmetic progressions.

Learn how to find the term of an arithmetic progression (AP) 2, 11, 20, 29, ... which is 290. Detailed step-by-step solution using the formula for the nth term of an AP. Suitable for students in Grades 7-9.

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