Find the 12th term of the geometric sequence shown below. 4x^(4),16x^(7),64x^(10),dots Answer:

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Find the 12th term of the geometric sequence shown below.  4x^(4),16x^(7),64x^(10),dots Answer:

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Identify common ratio: Identify the common ratio (r) of the geometric sequence by dividing the second term by the first term. Calculation: $ r = \frac{16x^7}{4x^4} = 4x^3 $Use nth term formula: Use the formula for the nth term of a geometric sequence, which is $ a_n = a_1 \cdot r^{(n-1)} $, where $ a_1 $ is the first term and $ n $ is the term number. Calculation: The first term $ a_1 $ is $ 4x^4 $, the common ratio $ r $ is $ 4x^3 $, and the term number $ n $ is 12.Substitute values: Substitute the values into the formula to find the 12th term. Calculation: $ a_{12} = 4x^4 \cdot (4x^3)^{11} $Simplify expression: Simplify the expression by applying the power to the common ratio. Calculation: $ a_{12} = 4x^4 \cdot 4^{11} \cdot x^{33} $Combine constants and terms: Combine the constants and the like terms. Calculation: $ a_{12} = 4^{12} \cdot x^{(4+33)} $Calculate final value: Calculate the value of $ 4^{12} $ and simplify the exponent for $ x $. Calculation: $ a_{12} = 16777216 \cdot x^{37} $

Find the $12$ th term of the geometric sequence shown below. $\newline$ $4 x^{4}, 16 x^{7}, 64 x^{10}, \ldots$ $\newline$ Answer:

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Find the 121212th term of the geometric sequence shown below.\newline4x4,16x7,64x10,… 4 x^{4}, 16 x^{7}, 64 x^{10}, \ldots 4x4,16x7,64x10,…\newlineAnswer:

Find the $12$ th term of the geometric sequence shown below. $\newline$ $4 x^{4}, 16 x^{7}, 64 x^{10}, \ldots$ $\newline$ Answer: