IXL - Convert a recursive formula to an explicit formula (Algebra 2 practice)

Use the initial term and the recursive formula to find an explicit formula for the sequence

Write your answer in simplest form.

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Learn with an example

question

Use the initial term and the recursive formula to find an explicit formula for the sequence

Write your answer in simplest form.

–

key idea

A sequence is an ordered list of numbers, called

terms.

The terms in a sequence are sometimes written

etc., where

is the first term,

is the second term, and so on. The subscript

on the term

is called the

index.

A recursive formula defines a sequence using earlier terms.

An explicit formula defines a sequence using only the index,

solution

Use the initial term

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and the recursive formula to write the first few terms of this sequence. Sometimes, the pattern can be easier to see if you don't simplify the terms.

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⋮

Each term is the sum of numbers, one of which is

–

and the rest of which are

–

Rewrite the terms using multiplication. (Recall that

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⋮

Relate the expressions to the indices.

–

(

–

)

–

(

–

)

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(

–

)

–

(

–

)

⋮

The first few terms satisfy the explicit formula

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(

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)

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Use substitution to verify that this explicit formula satisfies the recursive formula.

≟

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≟

[

–

(

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)

–

]

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≟

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This verifies that

–

satisfies the recursive formula

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The explicit formula is:

–

Looking for more? Try these:

Lesson: Arithmetic sequences

Lesson: Geometric sequences

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Teacher tools

Work it out

Not feeling ready yet? These can help:

MM.4Evaluate recursive formulas for sequences

MM.6Write a formula for an arithmetic sequence

MM.7Write a formula for a geometric sequence

Lesson: Arithmetic sequences

Lesson: Geometric sequences

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