If the ratio of consecutive terms in a geometric series is constant, what can be

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Question: If the ratio of consecutive terms in a geometric series is constant, what can be inferred about the series? (2023)

Options:

Correct Answer: It is exponential.

Exam Year: 2023

Solution:

A constant ratio of consecutive terms indicates that the series is exponential.

If the ratio of consecutive terms in a geometric series is constant, what can be inferred about the series? (2023)

If the ratio of consecutive terms in a geometric series is constant, what can be inferred about the series? (2023)

Step 1: Understand what a geometric series is. A geometric series is a sequence of numbers where each term after the first is found by multiplying the previous term by a fixed, non-zero number called the common ratio.
Step 2: Identify the meaning of 'consecutive terms'. Consecutive terms are terms that come one after the other in the series.
Step 3: Recognize that if the ratio of consecutive terms is constant, it means that if you take any term and divide it by the term before it, you will always get the same number (the common ratio).
Step 4: Conclude that because the ratio is constant, the series grows or shrinks at a consistent rate, which is characteristic of exponential growth or decay.
Step 5: Therefore, we can infer that the series is exponential.

Geometric Series – A geometric series is a sequence of numbers where each term after the first is found by multiplying the previous term by a fixed, non-zero number called the common ratio.
Constant Ratio – In a geometric series, the ratio of any term to its preceding term remains constant, which is a defining characteristic of the series.
Exponential Growth – The terms of a geometric series can be expressed as an exponential function, indicating that the series grows or decays exponentially based on the common ratio.