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The problem in the image is asking to find two numbers between 3 and 81 that form a geometric progression with 3 and 81.

### Let's break it down:

We are given the numbers 3 and 81, and we are asked to find two numbers in between them such that the sequence forms a geometric progression. A geometric progression (GP) follows the pattern:
\[ a, ar, ar^2, ar^3 \]
Where \(a\) is the first term, and \(r\) is the common ratio.

Given that the first term \(a = 3\), and the fourth term is \(ar^3 = 81\), we can solve for \(r\).

1. \( ar^3 = 81 \)
2. Since \( a = 3 \), we substitute:
   \[ 3r^3 = 81 \]
3. Dividing both sides by 3:
   \[ r^3 = 27 \]
4. Taking the cube root of both sides:
   \[ r = 3 \]

Now that we know the common ratio \(r = 3\), we can find the two numbers between 3 and 81.

### The terms of the progression are:
- First term: \( a = 3 \)
- Second term: \( ar = 3 \times 3 = 9 \)
- Third term: \( ar^2 = 3 \times 3^2 = 3 \times 9 = 27 \)
- Fourth term: \( ar^3 = 81 \)

So, the two numbers are **9** and **27**.

Would you like more details on geometric progression or any clarification?

### Related Questions:
1. What is the general formula for a geometric progression?
2. How do you calculate the sum of terms in a geometric progression?
3. Can a geometric progression have negative terms?
4. What is the difference between an arithmetic progression and a geometric progression?
5. How does the common ratio affect the growth of a geometric sequence?

### Tip:
In a geometric progression, if the ratio is greater than 1, the sequence grows exponentially. If the ratio is between 0 and 1, the terms decrease rapidly.

3 va 81 sonlari orasiga ikkita son shunday qo'yildiki, natijada bu to'rtta son geometrik progressiyani tashkil qildi. Bu sonlarni toping.

This problem asks you to find two numbers that form a geometric progression between 3 and 81. The step-by-step solution covers geometric progression formulas and the concept of common ratios, suitable for students in Grades 8-10.

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