What basic concept is required to solve for the last year in the geometric sequence related to the watch's value?

To solve for the last year in a geometric sequence, knowledge of geometric progression is essential.

A geometric sequence is characterized by each term being a constant multiple of the previous term. This concept allows us to calculate subsequent values in the sequence, which is crucial when considering the depreciation or appreciation of an item, such as a watch, over time. For example, if the value of the watch decreases by a fixed percentage each year, the situation can be modeled using a geometric progression where the first term is the initial value of the watch and the common ratio reflects the annual decrease in value.

Understanding this basic property enables you to establish a formula representing the value of the watch over time, allowing you to determine its value at the end of the desired period. Consequently, the correct answer revolves around knowing geometric progression, which directly applies to the context of the question regarding the watch's declining value. This understanding will allow you to calculate future values systematically and correctly interpret how they relate to each other over the specified term.