Choose the correct recursive formula for the following input-output pattern. Term Input Output 1st 1 3 2nd 2 6 3rd 3 12 4 24 5 48 6 96 a₁ = 3 {a₁ = =an-1 * 2, for n ≥ 3 a₁ = 2 =an-1*3 for n ≥ 2 a₁ = 3 =an-1 * 3, for n ≥ 3 a₁ = 3 +3, for n ≥ 3 O a O b Oc O {0₁₂ = {a₂² =an-1
Choose the correct recursive formula for the following input-output pattern. Term Input Output 1st 1 3 2nd 2 6 3rd 3 12 4 24 5 48 6 96 a₁ = 3 {a₁ = =an-1 * 2, for n ≥ 3 a₁ = 2 =an-1*3 for n ≥ 2 a₁ = 3 =an-1 * 3, for n ≥ 3 a₁ = 3 +3, for n ≥ 3 O a O b Oc O {0₁₂ = {a₂² =an-1
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
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![### Recursive Formulas for Input-Output Pattern
#### Problem Statement:
Choose the correct recursive formula for the following input-output pattern.
#### Input-Output Table:
| Term | Input | Output |
|-------|-------|--------|
| 1st | 1 | 3 |
| 2nd | 2 | 6 |
| 3rd | 3 | 12 |
| 4th | 4 | 24 |
| 5th | 5 | 48 |
| 6th | 6 | 96 |
#### Options for the Recursive Formula:
- **Option A**
\[
\begin{cases}
a_1 = 3 \\
a_n = a_{n-1} \times 2, \text{ for } n \geq 3
\end{cases}
\]
- **Option B**
\[
\begin{cases}
a_1 = 2 \\
a_n = a_{n-1} \times 3, \text{ for } n \geq 2
\end{cases}
\]
- **Option C**
\[
\begin{cases}
a_1 = 3 \\
a_n = a_{n-1} \times 3, \text{ for } n \geq 3
\end{cases}
\]
- **Option D**
\[
\begin{cases}
a_1 = 3 \\
a_n = a_{n-1} + 3, \text{ for } n \geq 3
\end{cases}
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Transcribed Image Text:### Recursive Formulas for Input-Output Pattern
#### Problem Statement:
Choose the correct recursive formula for the following input-output pattern.
#### Input-Output Table:
| Term | Input | Output |
|-------|-------|--------|
| 1st | 1 | 3 |
| 2nd | 2 | 6 |
| 3rd | 3 | 12 |
| 4th | 4 | 24 |
| 5th | 5 | 48 |
| 6th | 6 | 96 |
#### Options for the Recursive Formula:
- **Option A**
\[
\begin{cases}
a_1 = 3 \\
a_n = a_{n-1} \times 2, \text{ for } n \geq 3
\end{cases}
\]
- **Option B**
\[
\begin{cases}
a_1 = 2 \\
a_n = a_{n-1} \times 3, \text{ for } n \geq 2
\end{cases}
\]
- **Option C**
\[
\begin{cases}
a_1 = 3 \\
a_n = a_{n-1} \times 3, \text{ for } n \geq 3
\end{cases}
\]
- **Option D**
\[
\begin{cases}
a_1 = 3 \\
a_n = a_{n-1} + 3, \text{ for } n \geq 3
\end{cases}
\]
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