preceding term
[preceding term|preceding term] is a recursive formula that defines each term of a sequence using the preceding term(s).
Definition
preceding term is a recursive formula that defines each term of a sequence using the preceding term(s). The constant ratio between consecutive terms is maintained through recursive application.
Mechanism
preceding term To determine the common ratio, divide any term by the preceding term. This process applies to each term in the sequence. The mechanism involves dividing each term by its immediate predecessor to identify the ratio. The sequence's common ratio is established through this division method. Dividing each term by the preceding term consistently reveals the ratio.
Causes
preceding term Each successive term affects the sum less than the preceding term. The relationship between terms diminishes as the sequence progresses. This pattern indicates a decreasing influence of later terms on the overall total.
Effects
preceding term Each successive term affects the sum less than the preceding term. The preceding term has a greater impact on the total compared to subsequent terms. This pattern indicates diminishing influence as the sequence progresses. The relationship between terms shows decreasing contribution to the overall sum. The effect of each term diminishes relative to its position in the sequence.
Comparison
preceding term Each successive term has a diminishing impact on the sum compared to the preceding term. The effect of each subsequent term is less pronounced than the prior one. This pattern indicates that later terms contribute progressively smaller changes to the overall total. The relationship between terms shows that the influence of each new term is reduced relative to its predecessor. The diminishing influence of successive terms is evident in their reduced effect on the cumulative sum.