What is the 11th term of the sequence: 1, 3, 9, 27....?
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Correct Answer: Option D
Explanation:
To find the 11th term of the sequence \(1, 3, 9, 27, \ldots\), we note that it is a geometric sequence where:
- The first term \(a = 1\)
- The common ratio \(r = 3\)
The general term of a geometric sequence is given by:
\[ a_n = a \cdot r^{(n - 1)} \]
For the 11th term (\(n = 11\)):
\[ a_{11} = 1 \cdot 3^{(11 - 1)} \]
\[ a_{11} = 3^{10} \]
So, the 11th term of the sequence is \(3^{10}\).
Thus, the correct answer is:
D. \(3^{10}\)
To find the 11th term of the sequence \(1, 3, 9, 27, \ldots\), we note that it is a geometric sequence where:
- The first term \(a = 1\)
- The common ratio \(r = 3\)
The general term of a geometric sequence is given by:
\[ a_n = a \cdot r^{(n - 1)} \]
For the 11th term (\(n = 11\)):
\[ a_{11} = 1 \cdot 3^{(11 - 1)} \]
\[ a_{11} = 3^{10} \]
So, the 11th term of the sequence is \(3^{10}\).
Thus, the correct answer is:
D. \(3^{10}\)