What is the next term of the geometric sequence? 20,-10,5", "

Identify sequence type: Identify the type of sequence. The given sequence is 20, -10, 5, which changes sign and magnitude. This indicates that it is a geometric sequence because each term is multiplied by a common ratio to get the next term.Determine common ratio: Determine the common ratio of the sequence. To find the common ratio, divide the second term by the first term: (-10) / 20 = -1/2. Then, check this ratio by dividing the third term by the second term: 5 / (-10) = -1/2. Since the ratio is consistent, the common ratio is -1/2.Calculate next term: Calculate the next term in the sequence. To find the next term, multiply the last known term by the common ratio: 5 * (-1/2) = -2.5.

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What is the next term of the geometric sequence?

20,-10,5", "

What is the next term of the geometric sequence? $\newline$ $20, -10, 5,$

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

\newline

20, -10, 5,

Identify sequence type: Identify the type of sequence. $\newline$ The given sequence is $20$ , $-10$ , $5$ , which changes sign and magnitude. This indicates that it is a geometric sequence because each term is multiplied by a common ratio to get the next term.
Determine common ratio: Determine the common ratio of the sequence. $\newline$ To find the common ratio, divide the second term by the first term: $-\frac{10}{20} = -\frac{1}{2}$ . Then, check this ratio by dividing the third term by the second term: $\frac{5}{-10} = -\frac{1}{2}$ . Since the ratio is consistent, the common ratio is $-\frac{1}{2}$ .
Calculate next term: Calculate the next term in the sequence. $\newline$ To find the next term, multiply the last known term by the common ratio: $5 \times \left(-\frac{1}{2}\right) = -2.5$ .