In an Exponential (Geometric) Sequence, how is each term generated?

In an Exponential (Geometric) Sequence, how is each term generated?

• A. By adding a fixed amount to the previous term
• B. By multiplying the previous term by a fixed factor m
• C. By squaring the previous term
• D. By taking the reciprocal of the previous term

Answer: (B)

In a geometric sequence, each term is produced by multiplying the previous term by a fixed factor, called the common ratio. This means the next term is obtained by a_{n+1} = m · a_n, so the sequence looks like a_1, a_1·m, a_1·m^2, a_1·m^3, and so on. The constant factor m controls growth or decay: if m > 1 it grows, if 0 < m < 1 it shrinks, and if m is negative the terms alternate in sign. This multiplicative rule distinguishes it from an arithmetic sequence, where you add a fixed amount each step.

In a geometric sequence, each term is produced by multiplying the previous term by a fixed factor, called the common ratio. This means the next term is obtained by a_{n+1} = m · a_n, so the sequence looks like a_1, a_1·m, a_1·m^2, a_1·m^3, and so on. The constant factor m controls growth or decay: if m > 1 it grows, if 0 < m < 1 it shrinks, and if m is negative the terms alternate in sign. This multiplicative rule distinguishes it from an arithmetic sequence, where you add a fixed amount each step.