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Common Core (Functions)

Common Core for Mathematics

Examples, solutions, videos, and lessons to help High School students learn how to recognize that sequences are functions, sometimes defined recursively, whose domain is a subset of the integers.

For example, the Fibonacci sequence is defined recursively by

f(0) = f(1) = 1,

f(n+1) = f(n) + f(n-1) for n ≥ 1.

Common Core: HSF-IF.A.3

The following diagrams show Arithmetic Sequences as Linear Functions and Geometric Sequences as Exponential Functions. Scroll down the page for more examples and solutions.

**Sequences and Functions**

**Arithmetic Sequences as Linear Functions**

**Geometric Sequences as Exponential Functions**

**Arithmetic and Geometric Sequences**
**Arithmetic Sequences and Functions**

A(n) = A(1) + (n -1)d**Writing Arithmetic Sequences as Functions**

This video shows you how to view arithmetic sequences as functions, so that you can write a formula that'll give you any term of a sequence you want, just by plugging in the number of the term.**Arithmetic Sequences as Linear Functions**
**Recursive formulas for Arithmetic and Geometric Sequences**

Arithmetic Sequence: A(n) = A(1) + (n -1)d

Geometric Sequence: T(n) = T(n-1) × r**Recursive Functions Tutorial (With Fibonacci Sequence)**

This shows you how to solve recursive functions, using the example of the classic Fibonacci recursive function.

f(1) = 1

f(2) = 1

f(n) = f(n-2) + f(n-1)

You can use the free Mathway calculator and problem solver below to practice Algebra or other math topics. Try the given examples, or type in your own problem and check your answer with the step-by-step explanations.

Common Core (Functions)

Common Core for Mathematics

Examples, solutions, videos, and lessons to help High School students learn how to recognize that sequences are functions, sometimes defined recursively, whose domain is a subset of the integers.

For example, the Fibonacci sequence is defined recursively by

f(0) = f(1) = 1,

f(n+1) = f(n) + f(n-1) for n ≥ 1.

Common Core: HSF-IF.A.3

The following diagrams show Arithmetic Sequences as Linear Functions and Geometric Sequences as Exponential Functions. Scroll down the page for more examples and solutions.

A(n) = A(1) + (n -1)d

This video shows you how to view arithmetic sequences as functions, so that you can write a formula that'll give you any term of a sequence you want, just by plugging in the number of the term.

Arithmetic Sequence: A(n) = A(1) + (n -1)d

Geometric Sequence: T(n) = T(n-1) × r

This shows you how to solve recursive functions, using the example of the classic Fibonacci recursive function.

f(1) = 1

f(2) = 1

f(n) = f(n-2) + f(n-1)

Rotate to landscape screen format on a mobile phone or small tablet to use the **Mathway** widget, a free math problem solver that **answers your questions with step-by-step explanations**.

You can use the free Mathway calculator and problem solver below to practice Algebra or other math topics. Try the given examples, or type in your own problem and check your answer with the step-by-step explanations.

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