Arithmetic Sequence Formulas Flashcards

Vocabulary terms and mathematical formulas for arithmetic sequences based on the lesson concerning recursive and explicit expressions.

Recursive Formula

A formula that expresses each new term of a sequence based on the preceding term; to use it, you must know the value of the previous term.

Recursive Formula for an Arithmetic Sequence

$$a_n = a_{n-1} + d$$

$$a_n$$

The notation representing the $n$-th term in a sequence, which can be any position such as the first, second, or third term.

$$a_{n-1}$$

The notation representing the previous term in a sequence.

Common Difference ($d$)

The constant value added or subtracted in an arithmetic sequence to get from one term to the next.

Arithmetic Sequence

A sequence of numbers where each term is found by adding or subtracting a consistent common difference.

Explicit Formula

A formula used to calculate the $n$-th term of a sequence using only the term's position in the sequence, allowing you to find any term without knowing the previous one.

Explicit Formula for an Arithmetic Sequence

$$a_n = a_1 + d(n-1)$$

$$a_1$$

The notation representing the very first term in a sequence.

$$n$$

In sequence formulas, this represents the term's position in the sequence.