What is the next term of the geometric sequence? (81)/(25),(27)/(5),9

Identify Sequence Type: Identify whether the given sequence is geometric or arithmetic. In the given sequence, consecutive terms seem to have a common ratio. The given sequence is geometric.Find Common Ratio: Identify the common ratio of the sequence. To find the common ratio, divide the second term by the first term. (27/5) / (81/25) = (27/5) * (25/81) = (27*25) / (5*81) = (3^3*5^2) / (5*3^4) = 5/3 Common Ratio: 5/3Find Next Term: Find the next term in the sequence using the common ratio. The last term given in the sequence is 9. To find the next term, multiply the last term by the common ratio. 9 * (5/3) = (9/1) * (5/3) = (3*3) * (5/3) = 3 * 5 = 15 Next Term: 15

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What is the next term of the geometric sequence?

(81)/(25),(27)/(5),9

What is the next term of the geometric sequence? $\newline$ $(\frac{81}{25}),(\frac{27}{5}),9$

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Q. What is the next term of the geometric sequence?

\newline

(\frac{81}{25}),(\frac{27}{5}),9

Identify Sequence Type: Identify whether the given sequence is geometric or arithmetic. $\newline$ In the given sequence, consecutive terms seem to have a common ratio $r$ . $\newline$ The given sequence is geometric.
Find Common Ratio: Identify the common ratio of the sequence. $\newline$ To find the common ratio, divide the second term by the first term. $\newline$ $(\frac{27}{5}) / (\frac{81}{25}) = (\frac{27}{5}) \cdot (\frac{25}{81}) = (\frac{27\cdot25}{5\cdot81}) = (\frac{3^3\cdot5^2}{5\cdot3^4}) = \frac{5}{3}$ $\newline$ Common Ratio: $\frac{5}{3}$
Find Next Term: Find the next term in the sequence using the common ratio. $\newline$ The last term given in the sequence is $9$ . $\newline$ To find the next term, multiply the last term by the common ratio. $\newline$ $9 \times \left(\frac{5}{3}\right) = \left(\frac{9}{1}\right) \times \left(\frac{5}{3}\right) = \left(3\times3\right) \times \left(\frac{5}{3}\right) = 3 \times 5 = 15$ $\newline$ Next Term: $15$