Find the 12th term of Geometric Series 4, 8, 16, ...
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Find the 12th term of Geometric Series 4, 8, 16, ...
Try it .
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Answer:
To find the 12th term of a geometric series, you can use the formula for the nth term of a geometric sequence:
\[a_n = a_1 * r^(n-1)\]
Where:
- \(a_n\) is the nth term you want to find.
- \(a_1\) is the first term of the series.
- \(r\) is the common ratio.
- \(n\) is the term number.
In your series, the first term (\(a_1\)) is 4, and the common ratio (\(r\)) is 8 / 4 = 2 (each term is twice the previous term).
Now, plug these values into the formula to find the 12th term:
\[a_{12} = 4 * 2^(12-1)\]
\[a_{12} = 4 * 2^11\]
\[a_{12} = 4 * 2048\]
\[a_{12} = 8192\]
So, the 12th term of the geometric series 4, 8, 16, ... is 8192.
Step-by-step explanation:
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