Find the 9th term of the geometric sequence shown below. 7x^(3),-14x^(8),28x^(13),dots Answer:

Question

Find the 9th term of the geometric sequence shown below.  7x^(3),-14x^(8),28x^(13),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 = (-14x^(8)) / (7x^(3)) r = -2x^(5)Verify consistency: Verify the common ratio by dividing the third term by the second term to ensure it is consistent. Calculation: r = (28x^(13)) / (-14x^(8)) r = -2x^(5)Use nth term formula: Use the formula for the nth term of a geometric sequence, which is a_n = a_1 * r^(n-1), where a_1 is the first term and n is the term number. Calculation: a_9 = 7x^(3) * (-2x^(5))^(9-1)Simplify exponent: Simplify the exponent in the formula. Calculation: a_9 = 7x^(3) * (-2x^(5))^(8)Calculate power: Calculate the power of the common ratio. Calculation: (-2x^(5))^8 = (-2)^8 * (x^(5))^8 (-2)^8 = 256 (x^(5))^8 = x^(40)Multiply first term: Multiply the first term by the power of the common ratio. Calculation: a_9 = 7x^(3) * 256 * x^(40)Combine x terms: Combine the x terms by adding the exponents. Calculation: a_9 = 7 * 256 * x^(3+40) a_9 = 7 * 256 * x^(43)Multiply constants: Multiply the constants to find the 9th term. Calculation: a_9 = 7 * 256 * x^(43) a_9 = 1792 * x^(43)

Find the $9$ th term of the geometric sequence shown below. $\newline$ $7 x^{3},-14 x^{8}, 28 x^{13}, \ldots$ $\newline$ Answer:

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Find the $9$ th term of the geometric sequence shown below. $\newline$ $7 x^{3},-14 x^{8}, 28 x^{13}, \ldots$ $\newline$ Answer: