What is the next term of the geometric sequence? (27)/(16),-(9)/(4),3", "

Identify pattern in sequence: Identify the pattern in the sequence to determine if it is geometric. The given sequence is (27/16), -(9/4), 3. We need to check if there is a common ratio between the terms.Calculate common ratio: Calculate the common ratio by dividing the second term by the first term. Common ratio (r) = [-(9/4)] / [(27/16)] = -9/4 * 16/27 = -4/3Verify common ratio: Verify the common ratio by dividing the third term by the second term to ensure consistency. Common ratio check = 3 / [-(9/4)] = 3 * -4/9 = -4/3 Since the common ratio is consistent, we can confirm the sequence is geometric with a common ratio of -4/3.Find next term in sequence: Find the next term in the sequence by multiplying the last known term by the common ratio. Next term = 3 * (-4/3) = -4

Resources

Testimonials

Plans

Resources

Testimonials

Plans

AI tutor

Welcome to Bytelearn!

Let’s check out your problem:

What is the next term of the geometric sequence?

(27)/(16),-(9)/(4),3", "

What is the next term of the geometric sequence? $\frac{27}{16}, -\frac{9}{4}, 3$

View step-by-step help

Full solution

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

\frac{27}{16}, -\frac{9}{4}, 3

Identify pattern in sequence: Identify the pattern in the sequence to determine if it is geometric. $\newline$ The given sequence is $(\frac{27}{16}), -(\frac{9}{4}), 3$ . We need to check if there is a common ratio between the terms.
Calculate common ratio: Calculate the common ratio by dividing the second term by the first term. $\newline$ Common ratio $r$ = $\frac{-\left(\frac{9}{4}\right)}{\left(\frac{27}{16}\right)}$ = $-\frac{9}{4} \times \frac{16}{27}$ = $-\frac{4}{3}$
Verify common ratio: Verify the common ratio by dividing the third term by the second term to ensure consistency. $\newline$ Common ratio check = $\frac{3}{-\left(\frac{9}{4}\right)} = 3 \times -\frac{4}{9} = -\frac{4}{3}$ $\newline$ Since the common ratio is consistent, we can confirm the sequence is geometric with a common ratio of $-\frac{4}{3}$ .
Find next term in sequence: Find the next term in the sequence by multiplying the last known term by the common ratio. $\newline$ Next term = $$3$ \times \left(-\frac{$4$}{$3$}\right) = $-4$