Weaver Simmons
08/14/2023 · Elementary School
\( 4,12,36,108, \ldots \) What is the eighth term in this geometric sequence? In other words, what is \( u_{s} \) ?
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To find the eighth term in a geometric sequence, we need to identify the common ratio (\( r \)) first. The common ratio is found by dividing any term by its preceding term.
Given terms: 4, 12, 36, 108, ...
To find the common ratio (\( r \)):
\( r = \frac{12}{4} = 3 \)
Now that we have the common ratio, we can find the eighth term (\( u_{8} \)) using the formula for the nth term of a geometric sequence:
\( u_{n} = a \times r^{(n-1)} \)
Substitute the values:
\( u_{8} = 4 \times 3^{(8-1)} \)
\( u_{8} = 4 \times 3^{7} \)
Now, we can calculate the eighth term of the geometric sequence.
Calculate the value by following steps:
- step0: Calculate:
\(4\times 3^{7}\)
- step1: Evaluate the power:
\(4\times 2187\)
- step2: Multiply:
\(8748\)
The eighth term in the geometric sequence is 8748. Therefore, \( u_{8} = 8748 \).
Quick Answer
The eighth term is 8748.
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