A recursive formula is a formula that defines any term of a sequence in terms of its preceding term(s). For example: The recursive formula of an arithmetic sequence is, a n = a n-1 + d; The recursive formula of a geometric sequence is, a n = a n-1 r; Here, a n represents the n th term and a n-1 represents the (n-1) th term.

Write arithmetic and geometric sequences both recursively and with an explicit formula, use them to model situations, and translate between the two forms.

Recursive Formula – must know previous term *two formulas: arithmetic and geometric For an Arithmetic Sequence: t1 = 1 st term tn = t n-1 + d For a Geometric Sequence: t1 = 1 st term tn = r(t n-1) *Note: When writing the formula, the only thing you fill in is the 1 st term and either d or r. Explicit Formula – based on the term number.

Apr 1, 2025 · In this lesson, you will explore arithmetic and geometric sequences, distinguish them from other types of functions, and learn about their unique equations. The ability to translate a function will help you understand the structure of equations for sequences. For each of the following problems, a function is given.

This lesson will work with arithmetic sequences, their recursive and explicit formulas and finding terms in a sequence. In this lesson, it is assumed that you know what an arithmetic sequence is and can find a common difference.

Aug 30, 2024 · Recursive formulas and explicit formulas are two ways of expressing arithmetic and geometric sequences of numbers. In this video, we are going to discuss what each of them are and how to write sequences of numbers using each of these two techniques.

Jan 20, 2020 · Learn how to determine if a Sequence is Arithmetic or Geometric, find indicated terms, the general term, the Explicit Formula and the Recursive Formula.

Examples, solutions, videos, and lessons to help High School students learn how to write arithmetic and geometric sequences both recursively and with an explicit formula, use them to model situations, and translate between the two forms.

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Finding Common Differences. The values of the truck in the example are said to form an arithmetic sequence because they change by a constant amount each year. Each term increases or decreases by the same constant value called the common difference of the sequence. For this sequence, the common difference is –3,400.