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Computer Networking: A Top-Down Approach (7th Edition)
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**Algebra 27 - Educational Resource**

### Understanding Number Patterns in Arrays

An array consists of **consecutive positive numbers from 1 to 9 that repeat**. Here is how the array is structured:

- **Row 1** has one digit.
- **Row 2** has two digits.
- **Row 3** has four digits.
- **Row 4** has eight digits.

Each row contains double the number of digits as the previous row. 

#### Example:

- **Row 1**: 1
- **Row 2**: 2, 3
- **Row 3**: 4, 5, 6, 7
- **Row 4**: 8, 9, 1, 2, 3, 4, 5, 6

Incomplete array:
- **Row 5** and beyond would continue following the same pattern, doubling the number of digits consecutively.

### Questions:

a) **What is the 2020th number in the 2020th row?**
b) **What is the sum of the numbers in the 2020th row?**
c) **What is the nth number in the nth row?**
d) **What is the sum of the numbers in the nth row?**

Below the array, there are handwritten annotations indicating:
- "Digits double up."
- Calculations pointing to identifying values in row 2020 by first establishing values for row 2019, and then doubling those values for row 2020.

These problems require understanding the repetitive pattern and how the number of digits exponentially increases per row to derive the answers.
Transcribed Image Text:**Algebra 27 - Educational Resource** ### Understanding Number Patterns in Arrays An array consists of **consecutive positive numbers from 1 to 9 that repeat**. Here is how the array is structured: - **Row 1** has one digit. - **Row 2** has two digits. - **Row 3** has four digits. - **Row 4** has eight digits. Each row contains double the number of digits as the previous row. #### Example: - **Row 1**: 1 - **Row 2**: 2, 3 - **Row 3**: 4, 5, 6, 7 - **Row 4**: 8, 9, 1, 2, 3, 4, 5, 6 Incomplete array: - **Row 5** and beyond would continue following the same pattern, doubling the number of digits consecutively. ### Questions: a) **What is the 2020th number in the 2020th row?** b) **What is the sum of the numbers in the 2020th row?** c) **What is the nth number in the nth row?** d) **What is the sum of the numbers in the nth row?** Below the array, there are handwritten annotations indicating: - "Digits double up." - Calculations pointing to identifying values in row 2020 by first establishing values for row 2019, and then doubling those values for row 2020. These problems require understanding the repetitive pattern and how the number of digits exponentially increases per row to derive the answers.
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