What is the next term of the geometric sequence? -(16)/(5),8,-20", "

Identify sequence type: Identify the type of sequence. The given sequence has terms that are multiplied by a common ratio to get from one term to the next. This indicates that it is a geometric sequence.Determine common ratio: Determine the common ratio (r) of the sequence. To find the common ratio, divide the second term by the first term: r = 8 / (-(16/5)) = 8 * (-5/16) = -2.5 Similarly, check the ratio with the third and second term: r = -20 / 8 = -2.5 Since the common ratio is the same for both pairs of terms, the common ratio is confirmed to be -2.5.Calculate next term: Calculate the next term in the sequence using the common ratio. The next term is found by multiplying the last known term by the common ratio: Next term = -20 * (-2.5) = 50

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What is the next term of the geometric sequence?

-(16)/(5),8,-20", "

What is the next term of the geometric sequence? $\newline$ $-\frac{16}{5}$ , $8$ , $-20$

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

\newline

-\frac{16}{5}

8

-20

Identify sequence type: Identify the type of sequence. $\newline$ The given sequence has terms that are multiplied by a common ratio $r$ to get from one term to the next. This indicates that it is a geometric sequence.
Determine common ratio: Determine the common ratio $r$ of the sequence. $\newline$ To find the common ratio, divide the second term by the first term: $r = \frac{8}{-(\frac{16}{5})} = 8 \times (-\frac{5}{16}) = -2.5$ $\newline$ Similarly, check the ratio with the third and second term: $r = \frac{-20}{8} = -2.5$ $\newline$ Since the common ratio is the same for both pairs of terms, the common ratio is confirmed to be $-2.5$ .
Calculate next term: Calculate the next term in the sequence using the common ratio. $\newline$ The next term is found by multiplying the last known term by the common ratio: Next term = $-20 \times (-2.5) = 50$