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 the formula for common ratio

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

Step2: Calculate the ratio using the first two terms

Take the first two terms \( a_1 = 1.5 \) and \( a_2=1.2 \). Then \( r=\frac{a_2}{a_1}=\frac{1.2}{1.5} \).
Simplify \( \frac{1.2}{1.5} \): We can multiply numerator and denominator by 10 to get \( \frac{12}{15} \), and then divide numerator and denominator by 3, we get \( \frac{4}{5}=0.8 \).

Step3: Verify with other terms (optional but good practice)

Check with the second and third terms: \( a_2 = 1.2 \), \( a_3=0.96 \). Then \( r=\frac{a_3}{a_2}=\frac{0.96}{1.2} = 0.8 \).
Check with third and fourth terms: \( a_3 = 0.96 \), \( a_4 = 0.768 \). Then \( r=\frac{a_4}{a_3}=\frac{0.768}{0.96}=0.8 \). So the common ratio is \( 0.8 \).

Answer:

0.8