Question

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

Explanation:

Step1: Recall common ratio formula

The common ratio \( r \) of a geometric sequence is found by dividing a term by its previous term, i.e., \( r=\frac{a_{n}}{a_{n - 1}} \).

Step2: Calculate using first two terms

Take the second term \( 1.2 \) and divide by the first term \( 1.5 \): \( r=\frac{1.2}{1.5} \)
Simplify \( \frac{1.2}{1.5}=\frac{12}{15}=\frac{4}{5} = 0.8 \)

Step3: Verify with other terms

Check with third and second term: \( \frac{0.96}{1.2}=0.8 \), and fourth and third term: \( \frac{0.768}{0.96}=0.8 \). So the common ratio is \( 0.8 \).

Answer:

0.8