https://file.aiquickdraw.com/mathbot/file/17287852420698u3kmz1g.jpg

The problem from the image is written in Gujarati. Here's the translation and breakdown:

**Problem (translated):**
In an arithmetic progression (AP), the terms are 6, 7, \(x-2\), \(x\), 17, and the average (mean) of 16 and 20 is also given. Find \(x\).

### Step-by-step solution:

1. The terms are part of an arithmetic progression (AP): \(6, 7, x-2, x, 17\).
2. In an AP, the difference between consecutive terms is constant, known as the common difference (\(d\)).
   - Difference between the first and second term: \(7 - 6 = 1\), so \(d = 1\).

3. Since the progression continues:
   \[
   (x-2) - 7 = 1 \quad \text{(because the common difference is 1)}
   \]
   Solve for \(x-2\):
   \[
   x - 2 = 8 \quad \Rightarrow \quad x = 10
   \]

Thus, the value of \(x\) is **10**.

Would you like more details or have any further questions?

Here are 5 related questions you can explore:
1. What is the general formula for the nth term in an arithmetic progression?
2. How do you calculate the sum of the first n terms in an arithmetic progression?
3. What other methods could be used to solve this kind of AP problem?
4. How can you determine if a sequence is an arithmetic progression?
5. What are some real-world applications of arithmetic progressions?

**Tip:** In an AP, the common difference is key—once you know it, you can find unknown terms and solve for variables quickly.

In an arithmetic progression (AP), the terms are 6, 7, x-2, x, 17, and the average of 16 and 20 is also given. Find x.

Solve for x in the arithmetic progression with terms 6, 7, x-2, x, and 17. Learn how to apply the concept of common difference to find unknown terms in the sequence. Suitable for students in Grades 8-10.

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