Write the first five terms of the sequence. Determine whether or not the sequence is arithmetic.

step 1 Okay, here in this case we just need to find the first five term of the sequence. If the sequenc

Write the first five terms of the sequence. Determine...

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Key Concepts

Sequence

A sequence is an ordered list of numbers defined by a specific rule or formula. In many mathematical contexts, each term of the sequence is generated by applying the given rule to its position in the list, thus establishing a predictable pattern or relationship among the terms.

Arithmetic Sequence

An arithmetic sequence is a type of sequence in which each term after the first is obtained by adding a constant value, known as the common difference, to the preceding term. This property leads to a consistent difference between any consecutive terms throughout the entire sequence.

Common Difference

The common difference in an arithmetic sequence is the fixed amount added to each term to get the next term. It is found by subtracting any term from the term that follows it, and this difference remains constant across the sequence if the sequence is indeed arithmetic.

Alternating Sequence

An alternating sequence is one where the signs of the terms change in a regular pattern, often due to factors like (-1)^n in the formula. This results in a sequence where the terms may alternate between two values or follow a specific dual-pattern behavior, which is a central characteristic in sequences involving alternating signs.

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