https://file.aiquickdraw.com/mathbot/file/1728997190512pu3lr9q8.jpg

رابطه بین الگوها را بدست آورید

The image you provided appears to be a page from a math textbook in Persian, likely focused on identifying patterns and calculating totals based on visual representations of circles or dots.

Here is a summary of the tasks presented:

1. **Pattern Recognition**: The exercise shows various groups of circles (or dots) and asks students to determine how many circles would be in the seventh pattern (شکل هفتم). It encourages students to analyze how the numbers of circles are increasing across the patterns.

2. **Guided Solution**: 
   - The solution method involves grouping the circles and counting them step-by-step, showing how the number of circles increases in each shape.
   - A pattern is identified (7 + 8 = 15 circles in the seventh shape), and various approaches to finding this total are explained.

3. **Exercise Questions**: 
   - You are asked if you can find another method to solve the problem.
   - You are also prompted to consider whether the pattern could hold beyond these examples and to calculate the total number of circles for other shapes.

### Finding the Pattern:
The number of circles increases with each subsequent pattern. For example:
- The first shape has 1 circle.
- The second shape has 3 circles.
- The third shape has 6 circles, and so on.

The number of circles increases in a triangular number pattern, where the total number of circles for shape \(n\) can be given by:
\[
T_n = \frac{n(n+1)}{2}
\]
So, for the seventh shape (\(n = 7\)):
\[
T_7 = \frac{7(7+1)}{2} = \frac{7 \times 8}{2} = 28 \text{ circles}
\]

Would you like more details on any part of this problem? Let me know if you have any specific questions!

### Relative Questions:
1. Can you identify the formula used to calculate the number of circles in each shape?
2. How does the number of circles grow in each step of the pattern?
3. What is the significance of the grouping method shown in the solution?
4. How would you extend this pattern to the 10th shape?
5. Can you think of a different way to group or count the circles?

### Tip:
Recognizing triangular numbers is key when solving pattern problems where growth follows this specific type of sequence!

Determine the relationship between the patterns and find the number of circles in the seventh pattern.

In this problem, students explore pattern recognition by calculating the number of circles in a growing sequence. Learn how to apply basic addition and identify visual growth patterns, suitable for Grades 2-4.

Math Problem Statement

Solution

Ask a new question for Free

By Image

Math Problem Analysis

Mathematical Concepts

Formulas

Theorems

Suitable Grade Level

Related Recommendation