To determine the common ratio in the given sequence \(1.5, 1.2, 0.96, 0.768, \ldots\), we can divide each term by its preceding term.
1. Calculate the ratio of the second term to the first term:
\[
\frac{1.2}{1.5} = \frac{4}{5} = 0.8
\]
2. Calculate the ratio of the third term to the second term:
\[
\frac{0.96}{1.2} = \frac{0.96 \div 0.12}{1.2 \div 0.12} = \frac{8}{10} = 0.8
\]
3. Calculate the ratio of the fourth term to the third term:
\[
\frac{0.768}{0.96} = \frac{0.768 \div 0.96}{0.96 \div 0.96} = \frac{8}{10} = 0.8
\]
Since the ratio between each pair of successive terms is consistent, the common ratio is \(0.8\).
Thus, the common ratio is:
\[
\boxed{0.8}
\]
What is the common ratio between successive terms in the sequence?
1.5, 1.2, 0.96, 0.768, …
–0.8
–0.3
0.3
0.8
1 answer