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The question asks to find the first term in an arithmetic progression (AP) that has 4 digits. The given sequence is:

\[ 8, 11, 14, \dots \]

In this arithmetic progression:
- The first term \( a = 8 \)
- The common difference \( d = 11 - 8 = 3 \)

The formula for the \(n\)-th term of an arithmetic progression is:

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

We are asked to find the value of \(n\) such that \(a_n\) is the first term with 4 digits. This means \(a_n \geq 1000\).

Substitute the values for \(a\) and \(d\):

\[
a_n = 8 + (n - 1) \cdot 3
\]

We want \(a_n \geq 1000\):

\[
8 + (n - 1) \cdot 3 \geq 1000
\]

Now, let's solve for \(n\).The equation gives \( n = \frac{995}{3} \), which is approximately 331.67. Since \( n \) must be an integer, we round up to the next whole number, which is \( n = 332 \).

Thus, the first term of the arithmetic progression with 4 digits occurs when \( n = 332 \).

Do you want further clarification or details on this? 

Here are 5 related questions to explore:
1. How can I verify that \( n = 332 \) is the correct value?
2. What is the general formula for the sum of an arithmetic progression?
3. How does changing the common difference \(d\) affect the \(n\)-th term?
4. How can I find the number of terms in an arithmetic progression?
5. What if the progression had a negative common difference?

**Tip:** Always remember to check whether the result for \(n\) needs to be rounded up or down based on the problem requirements.

nth term of the given arithmetic progression is the first to have 4 digits. 8, 11, 14, ... Find the value of n.

Learn how to calculate the nth term in an arithmetic progression (AP) where the sequence 8, 11, 14,... results in the first term having 4 digits. This detailed solution is suitable for Grades 8-10 and covers the nth term formula for arithmetic progressions.

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