What is the next term of the geometric sequence? -(128)/(27),(32)/(9),-(8)/(3)", "

Identify the pattern: Identify the pattern in the sequence. The given sequence is -(128/27), (32/9), -(8/3). We need to determine if this is a geometric sequence and, if so, find the common ratio.Calculate the common ratio: Calculate the common ratio. To find the common ratio, we divide the second term by the first term and the third term by the second term. (32/9) / (-(128/27)) = (32/9) * (-(27/128)) = -1/3 -(8/3) / (32/9) = -(8/3) * (9/32) = -1/3 The common ratio is -1/3.Find the next term: Find the next term in the sequence. To find the next term, we multiply the last known term by the common ratio. Next term = -(8/3) * (-1/3) = 8/9

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What is the next term of the geometric sequence?

-(128)/(27),(32)/(9),-(8)/(3)", "

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Identify the pattern: Identify the pattern in the sequence. $\newline$ The given sequence is $-(128/27)$ , $(32/9)$ , $-(8/3)$ . We need to determine if this is a geometric sequence and, if so, find the common ratio.
Calculate the common ratio: Calculate the common ratio. $\newline$ To find the common ratio, we divide the second term by the first term and the third term by the second term. $\newline$ $(\frac{32}{9}) / (-(\frac{128}{27})) = (\frac{32}{9}) \cdot (-(\frac{27}{128})) = -\frac{1}{3}$ $\newline$ $-(\frac{8}{3}) / (\frac{32}{9}) = -(\frac{8}{3}) \cdot (\frac{9}{32}) = -\frac{1}{3}$ $\newline$ The common ratio is $-\frac{1}{3}$ .
Find the next term: Find the next term in the sequence. $\newline$ To find the next term, we multiply the last known term by the common ratio. $\newline$ Next term = $-(\frac{8}{3}) \times (-\frac{1}{3}) = \frac{8}{9}$