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.