What is the next term of the geometric sequence? -(1)/(7),(4)/(7),-(16)/(7)", "

Identify pattern in sequence: Identify the pattern in the sequence to determine if it is geometric. The sequence is given as: -(1/7), (4/7), -(16/7) We can see that each term is obtained by multiplying the previous term by a common ratio.Find common ratio: Find the common ratio by dividing the second term by the first term. Common ratio (r) = (4/7) / (-(1/7)) = -4Verify common ratio: Verify the common ratio by dividing the third term by the second term to ensure consistency. Check ratio = (-(16/7)) / (4/7) = -4 The common ratio is consistent, confirming that the sequence is geometric with a common ratio of -4.Calculate next term: Calculate the next term by multiplying the last known term by the common ratio. Next term = -(16/7) * -4 = 64/7

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What is the next term of the geometric sequence?

-(1)/(7),(4)/(7),-(16)/(7)", "

What is the next term of the geometric sequence? $\newline$ $-\frac{1}{7}$ , $\frac{4}{7}$ , $-\frac{16}{7}$

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

\newline

-\frac{1}{7}

\frac{4}{7}

-\frac{16}{7}

Identify pattern in sequence: Identify the pattern in the sequence to determine if it is geometric. $\newline$ The sequence is given as: $-(\frac{1}{7})$ , $(\frac{4}{7})$ , $-(\frac{16}{7})$ $\newline$ We can see that each term is obtained by multiplying the previous term by a common ratio.
Find common ratio: Find the common ratio by dividing the second term by the first term. $\newline$ Common ratio $r$ = $\frac{4}{7}$ / $\frac{-(1)}{7}$ = $-4$
Verify common ratio: Verify the common ratio by dividing the third term by the second term to ensure consistency. $\newline$ Check ratio = $\left(-\frac{16}{7}\right) \div \left(\frac{4}{7}\right) = -4$ $\newline$ The common ratio is consistent, confirming that the sequence is geometric with a common ratio of $-4$ .
Calculate next term: Calculate the next term by multiplying the last known term by the common ratio. $\newline$ Next term = $-(\frac{16}{7}) \times -4 = \frac{64}{7}$