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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