What is the 10th term of the sequence 3, 12, 48, 192,...? 0 3,145,728 786,432 1,048,576 924,346
What is the 10th term of the sequence 3, 12, 48, 192,...? 0 3,145,728 786,432 1,048,576 924,346
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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Answer this question “CORRECTLY”!!!
![What is the 10th term of the sequence \(3, \ 12, \ 48, \ 192, \ldots\) ?
- \(3,145,728\)
- \(786,432\)
- \(1,048,576\)
- \(924,346\)
This problem asks for the 10th term in a geometric sequence. To solve this, first observe the pattern:
- The sequence starts at 3.
- Multiply 3 by 4 to get the second term: \(3 \times 4 = 12\).
- Multiply 12 by 4 to get the third term: \(12 \times 4 = 48\).
- Continue this pattern of multiplying by 4.
The sequence follows the formula:
\[ a_n = 3 \times 4^{(n-1)} \]
To find the 10th term:
\[ a_{10} = 3 \times 4^{9} \]
Calculating the 10th term will require evaluating \(4^9\) and then multiplying by 3 to find the correct choice from the given options.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F944b0b3b-c481-4a1c-a28c-b41af101c131%2F4b58644e-0f55-4c90-a07c-95c7f96b1c63%2F3toxkj_processed.jpeg&w=3840&q=75)
Transcribed Image Text:What is the 10th term of the sequence \(3, \ 12, \ 48, \ 192, \ldots\) ?
- \(3,145,728\)
- \(786,432\)
- \(1,048,576\)
- \(924,346\)
This problem asks for the 10th term in a geometric sequence. To solve this, first observe the pattern:
- The sequence starts at 3.
- Multiply 3 by 4 to get the second term: \(3 \times 4 = 12\).
- Multiply 12 by 4 to get the third term: \(12 \times 4 = 48\).
- Continue this pattern of multiplying by 4.
The sequence follows the formula:
\[ a_n = 3 \times 4^{(n-1)} \]
To find the 10th term:
\[ a_{10} = 3 \times 4^{9} \]
Calculating the 10th term will require evaluating \(4^9\) and then multiplying by 3 to find the correct choice from the given options.
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