Burton Schneider
11/16/2023 · High School

Find the \( 10^{\text {th }} \) term of the following geometric sequence. \[ 7,28,112,448, \ldots \]

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To find the 10th term of a geometric sequence, we need to know the first term and the common ratio. Given geometric sequence: 7, 28, 112, 448, ... First term (a) = 7 Common ratio (r) = 28/7 = 4 The formula to find the nth term of a geometric sequence is: \[ a_n = a \times r^{(n-1)} \] Substitute the values: \[ a_{10} = 7 \times 4^{(10-1)} \] Now, calculate the 10th term. Calculate the value by following steps: - step0: Calculate: \(7\times 4^{10-1}\) - step1: Subtract the numbers: \(7\times 4^{9}\) The 10th term of the geometric sequence is 1835008.

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The 10th term is 1835008.
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