https://file.aiquickdraw.com/mathbot/file/17291030750307trpfep4.jpg

In the image, you are asked to determine how many triangles there are in **pattern number 80** from a sequence of patterns made from hexagons and triangles. 

### Analysis of the Problem:
- Each pattern contains hexagons and triangles.
- The image suggests that the number of triangles in each pattern increases linearly.
  
Looking at the patterns:
1. **Pattern 1** has 1 triangle.
2. **Pattern 2** has 3 triangles.
3. **Pattern 3** has 5 triangles.
4. **Pattern 4** has 7 triangles.

We can see that the number of triangles increases by 2 for each pattern. This forms an arithmetic sequence where the difference between consecutive terms is 2.

### Formula for the nth term of an arithmetic sequence:
The nth term of an arithmetic sequence can be calculated as:
\[
T_n = T_1 + (n - 1) \cdot d
\]
Where:
- \(T_1 = 1\) (the first term),
- \(d = 2\) (the common difference),
- \(n = 80\) (the pattern number we need to find).

### Substituting the values:
\[
T_{80} = 1 + (80 - 1) \cdot 2
\]
\[
T_{80} = 1 + 79 \cdot 2
\]
\[
T_{80} = 1 + 158 = 159
\]

### Conclusion:
There are **159 triangles** in pattern number 80.

---

Would you like more details on the arithmetic sequence or have any other questions?

### Related Questions:
1. What is the formula to find the number of hexagons in pattern number 80?
2. How do arithmetic sequences apply to real-world problems?
3. Can we derive a general formula for the total number of shapes (hexagons + triangles) in any pattern number?
4. What if the number of triangles increased by a different value? How would the sequence change?
5. How many triangles would be there in pattern number 100?

### Tip:
Always check the pattern carefully to identify the common difference in arithmetic sequences, as this helps in forming the correct equation for the nth term.

How many triangles are there in pattern number 80?

Learn how to find the number of triangles in pattern number 80 using arithmetic sequences. This problem explores the pattern of adding triangles and uses the arithmetic sequence formula to solve for the 80th term. Perfect for students in Grades 6-8.

Math Problem Statement

Solution

Ask a new question for Free

By Image

Math Problem Analysis

Mathematical Concepts

Formulas

Theorems

Suitable Grade Level

Related Recommendation