Answer :
Let's interpret and rewrite the given numerical patterns step-by-step to understand and analyze them clearly.
### Step 1: Understand Each Line of the Pattern
We are given several lines of numbers and symbols. Let's break down each line:
1. First Line:
[tex]\[ 15 = 3 - 31 - 38 - 46 \][/tex]
This line appears to be a sequence of numbers connected by subtraction and an equality sign.
2. Second Line:
[tex]\[ 20 - 40 - 60 \sim 80 \][/tex]
This line contains numbers connected by subtraction and a similarity sign ("∼").
3. Third Line:
[tex]\[ -2 - 4 - 6 - 8 - 10 - 12 \][/tex]
This line contains a sequence of numbers all connected by subtraction.
4. Fourth Line:
[tex]\[ -14 - 16 \][/tex]
This line contains two numbers connected by subtraction.
5. Fifth Line:
[tex]\[ 15 - 25 - 35 - 45 - 55 - \][/tex]
This line contains a sequence of numbers all connected by subtraction and it ends with a subtraction sign.
6. Sixth Line:
[tex]\[ 65 - 75 \][/tex]
This line contains two numbers connected by subtraction.
### Step 2: Combining and Interpreting the Patterns
Let's combine and rewrite the given numerical series comprehensively.
### Numerical Patterns Interpretation
#### First Line
[tex]\[ 15 = 3 - 31 - 38 - 46 \][/tex]
This suggests that 15 is the result after the operations [tex]\(3 - 31 - 38 - 46\)[/tex].
#### Second Line
[tex]\[ 20 - 40 - 60 \sim 80 \][/tex]
Here, [tex]\(20, 40,\)[/tex] and [tex]\(60\)[/tex] are involved in subtractions, followed by a similarity symbol [tex]\(\sim\)[/tex] and [tex]\(80\)[/tex].
#### Third Line
[tex]\[ -2 - 4 - 6 - 8 - 10 - 12 \][/tex]
A continuous series of numbers with negative values subtracted from each other.
#### Fourth Line
[tex]\[ -14 - 16 \][/tex]
Two negative values subtracted from each other.
#### Fifth Line
[tex]\[ 15 - 25 - 35 - 45 - 55 - \][/tex]
A sequence of numbers increasing by 10 and connected by subtractions, ending with a subtraction sign.
#### Sixth Line
[tex]\[ 65 - 75 \][/tex]
This connects two numbers with a subtraction sign.
### Summary
The patterns convey sequences and operations on numbers. Each line follows a certain structure of subtractions:
1. The first line equates a sequence of subtractions to a number.
2. The second line follows a sequence ending differently with a similarity sign.
3. The third and fourth lines are entirely subtraction sequences.
4. The fifth line begins an increasing sequence that ends with a subtraction sign.
5. The sixth line concludes with a simple subtractive relation.
Each step involves understanding how numbers are connected through operations to form the sequences. These patterns show relationships between numbers through arithmetic operations in a structured manner.
### Step 1: Understand Each Line of the Pattern
We are given several lines of numbers and symbols. Let's break down each line:
1. First Line:
[tex]\[ 15 = 3 - 31 - 38 - 46 \][/tex]
This line appears to be a sequence of numbers connected by subtraction and an equality sign.
2. Second Line:
[tex]\[ 20 - 40 - 60 \sim 80 \][/tex]
This line contains numbers connected by subtraction and a similarity sign ("∼").
3. Third Line:
[tex]\[ -2 - 4 - 6 - 8 - 10 - 12 \][/tex]
This line contains a sequence of numbers all connected by subtraction.
4. Fourth Line:
[tex]\[ -14 - 16 \][/tex]
This line contains two numbers connected by subtraction.
5. Fifth Line:
[tex]\[ 15 - 25 - 35 - 45 - 55 - \][/tex]
This line contains a sequence of numbers all connected by subtraction and it ends with a subtraction sign.
6. Sixth Line:
[tex]\[ 65 - 75 \][/tex]
This line contains two numbers connected by subtraction.
### Step 2: Combining and Interpreting the Patterns
Let's combine and rewrite the given numerical series comprehensively.
### Numerical Patterns Interpretation
#### First Line
[tex]\[ 15 = 3 - 31 - 38 - 46 \][/tex]
This suggests that 15 is the result after the operations [tex]\(3 - 31 - 38 - 46\)[/tex].
#### Second Line
[tex]\[ 20 - 40 - 60 \sim 80 \][/tex]
Here, [tex]\(20, 40,\)[/tex] and [tex]\(60\)[/tex] are involved in subtractions, followed by a similarity symbol [tex]\(\sim\)[/tex] and [tex]\(80\)[/tex].
#### Third Line
[tex]\[ -2 - 4 - 6 - 8 - 10 - 12 \][/tex]
A continuous series of numbers with negative values subtracted from each other.
#### Fourth Line
[tex]\[ -14 - 16 \][/tex]
Two negative values subtracted from each other.
#### Fifth Line
[tex]\[ 15 - 25 - 35 - 45 - 55 - \][/tex]
A sequence of numbers increasing by 10 and connected by subtractions, ending with a subtraction sign.
#### Sixth Line
[tex]\[ 65 - 75 \][/tex]
This connects two numbers with a subtraction sign.
### Summary
The patterns convey sequences and operations on numbers. Each line follows a certain structure of subtractions:
1. The first line equates a sequence of subtractions to a number.
2. The second line follows a sequence ending differently with a similarity sign.
3. The third and fourth lines are entirely subtraction sequences.
4. The fifth line begins an increasing sequence that ends with a subtraction sign.
5. The sixth line concludes with a simple subtractive relation.
Each step involves understanding how numbers are connected through operations to form the sequences. These patterns show relationships between numbers through arithmetic operations in a structured manner.
