what is the common ratio between successive terms in the sequence?\n1.5, 1.2, 0.96, 0.768…

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