Q6. What is a11 for the geometric sequence with a₁ = 4 and r = 4?
Advanced Engineering Mathematics
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ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
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![**Question 6**: What is \( a_{11} \) for the geometric sequence with \( a_1 = 4 \) and \( r = 4 \)?
In a geometric sequence, the nth term can be found using the formula:
\[
a_n = a_1 \cdot r^{(n-1)}
\]
For this specific sequence:
- The first term \( a_1 = 4 \)
- The common ratio \( r = 4 \)
To find \( a_{11} \):
\[
a_{11} = 4 \cdot 4^{(11-1)} = 4 \cdot 4^{10}
\]
Calculate \( 4^{10} \) and multiply by 4 to find \( a_{11} \).](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Fbc6fbff9-4759-45b9-9f61-27046377aa96%2Fab6d5156-89aa-47a7-8352-d927360f0e75%2Ftfo01vc_processed.jpeg&w=3840&q=75)
Transcribed Image Text:**Question 6**: What is \( a_{11} \) for the geometric sequence with \( a_1 = 4 \) and \( r = 4 \)?
In a geometric sequence, the nth term can be found using the formula:
\[
a_n = a_1 \cdot r^{(n-1)}
\]
For this specific sequence:
- The first term \( a_1 = 4 \)
- The common ratio \( r = 4 \)
To find \( a_{11} \):
\[
a_{11} = 4 \cdot 4^{(11-1)} = 4 \cdot 4^{10}
\]
Calculate \( 4^{10} \) and multiply by 4 to find \( a_{11} \).
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