Find the 11th term of the geometric sequence shown below. -6x^(8),18x^(10),-54x^(12),dots Answer:

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Find the 11th term of the geometric sequence shown below.  -6x^(8),18x^(10),-54x^(12),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{18x^{10}}{-6x^8} = -3x^2 $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: We need to find the 11th term, so $ n = 11 $.Substitute values: Substitute the known values into the formula to find the 11th term. Calculation: $ a_{11} = -6x^8 \cdot (-3x^2)^{(11-1)} $Simplify exponent: Simplify the exponent in the formula. Calculation: $ a_{11} = -6x^8 \cdot (-3x^2)^{10} $Calculate power: Calculate the power of $ -3x^2 $ raised to the 10th power. Calculation: $ (-3x^2)^{10} = (-3)^{10} \cdot (x^2)^{10} $Simplify powers: Simplify the powers. Calculation: $ (-3)^{10} = 59049 $ and $ (x^2)^{10} = x^{20} $Multiply by first term: Multiply the simplified powers by the first term to get the 11th term. Calculation: $ a_{11} = -6x^8 \cdot 59049 \cdot x^{20} $Combine x terms: Combine the x terms by adding the exponents. Calculation: $ a_{11} = -6 \cdot 59049 \cdot x^{8+20} $Simplify multiplication: Simplify the multiplication to find the 11th term. Calculation: $ a_{11} = -6 \cdot 59049 \cdot x^{28} $Calculate product: Calculate the product of -6 and 59049. Calculation: $ a_{11} = -354294 \cdot x^{28} $

Find the $11$ th term of the geometric sequence shown below. $\newline$ $-6 x^{8}, 18 x^{10},-54 x^{12}, \ldots$ $\newline$ Answer:

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Find the 111111th term of the geometric sequence shown below.\newline−6x8,18x10,−54x12,… -6 x^{8}, 18 x^{10},-54 x^{12}, \ldots −6x8,18x10,−54x12,…\newlineAnswer:

Find the $11$ th term of the geometric sequence shown below. $\newline$ $-6 x^{8}, 18 x^{10},-54 x^{12}, \ldots$ $\newline$ Answer: