What is the next term of the geometric sequence? (40)/(27),(20)/(9),(10)/(3)", "

Identify Sequence Type: Identify whether the given sequence is geometric or arithmetic. The given sequence has terms that are each a constant factor of the previous term, which indicates that it is a geometric sequence.Find Common Ratio: Identify the common ratio of the geometric sequence. To find the common ratio, divide the second term by the first term. Common Ratio (r) = (20/9) / (40/27) = (20/9) * (27/40) = (2/1) * (3/4) = 6/4 = 3/2Calculate Next Term: Find the next term in the sequence using the common ratio. The last term given in the sequence is (10/3). To find the next term, multiply the last term by the common ratio. Next Term = (10/3) * (3/2) = (10/1) * (1/2) = 10/2 = 5

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What is the next term of the geometric sequence?

(40)/(27),(20)/(9),(10)/(3)", "

What is the next term of the geometric sequence? $\newline$ $\frac{40}{27}$ , $\frac{20}{9}$ , $\frac{10}{3}$

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

\newline

\frac{40}{27}

\frac{20}{9}

\frac{10}{3}

Identify Sequence Type: Identify whether the given sequence is geometric or arithmetic. $\newline$ The given sequence has terms that are each a constant factor of the previous term, which indicates that it is a geometric sequence.
Find Common Ratio: Identify the common ratio of the geometric sequence. $\newline$ To find the common ratio, divide the second term by the first term. $\newline$ Common Ratio $r$ = $\frac{20}{9}$ / $\frac{40}{27}$ = $\frac{20}{9}$ * $\frac{27}{40}$ = $\frac{2}{1}$ * $\frac{3}{4}$ = $\frac{6}{4}$ = $\frac{3}{2}$
Calculate Next Term: Find the next term in the sequence using the common ratio. $\newline$ The last term given in the sequence is $(10/3)$ . To find the next term, multiply the last term by the common ratio. $\newline$ Next Term = $(10/3) \times (3/2) = (10/1) \times (1/2) = 10/2 = 5$