Question

what does the variable r represent in the geometric sequence formula ( a_n = a_1 cdot r^{(n - 1)} )?
a. the common ratio
b. the common difference
c. the first term
d. the number of terms

Explanation:

In a geometric sequence formula \(a_n = a_1 \cdot r^{(n - 1)}\), we recall the definitions of each component:

• The common difference is for arithmetic sequences, not geometric, so option b is incorrect.
• The first term is \(a_1\), so option c is incorrect.
• The number of terms is \(n\), so option d is incorrect.
• The variable \(r\) is defined as the common ratio, which is the factor by which each term is multiplied to get the next term in the geometric sequence. So option a is correct.

Answer:

a. The common ratio