Write an expression for the apparent n th term of the sequence. (Assume n begins with 1 .) (1)/(

step 1 In this sequence, we know that the first term is positive and second term is negative and third

Write an expression for the apparent n th term of the...

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Key Concepts

Sequence

A sequence is an ordered list of numbers or objects arranged by a particular rule. Understanding sequences includes knowing how each term relates to its position in the list and how to generate them based on a defined pattern.

Geometric Sequence

A geometric sequence is a type of sequence where each term is produced by multiplying the previous term by a constant factor called the common ratio. This structure allows for the concise representation of any term in the sequence if the first term and the common ratio are known.

Alternating Signs

An alternating sequence features terms that switch between positive and negative values. This behavior is typically expressed with a factor like (-1) raised to a power that depends on the term's position, ensuring that the sign of each term alternates in a predictable pattern.

Nth Term Expression

The nth term expression is a formula that allows one to compute any term in a sequence directly by its position, without needing to generate all preceding terms. In the context of geometric sequences, it generally utilizes the first term multiplied by the common ratio raised to the (n - 1) power, sometimes modified to account for alternating signs.

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