IXL - Convert an explicit formula to a recursive formula (Algebra 1 practice)

Use the explicit formula to find a recursive formula for the sequence

Write your answer in simplest form.

The recursive formula should depend on

–

ref_doc_title.

Learn with an example

question

Use the explicit formula to find a recursive formula for the sequence

Write your answer in simplest form.

The recursive formula should depend on

–

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.

An explicit formula defines a sequence using only the index,

A recursive formula defines a sequence using earlier terms.

solution

Use the explicit formula to find the first few terms of this sequence, starting with

Plug

into the formula

–

Now find

Plug

into the formula

–

Continue this process. The first 6 terms are given in the table below.

n	a n
1	– 37
2	– 54
3	– 71
4	– 88
5	– 105
6	– 122

To find the recursive formula, start by looking at the differences of consecutive terms. In this case, the differences between consecutive terms are all the same. (Notice that

–

has no value for

since there is no

The first term in the sequence is

n	a n	a n – a n – 1
2	– 54	– 17
3	– 71	– 17
4	– 88	– 17
5	– 105	– 17
6	– 122	– 17

This table shows that

–

for

≤

so the first few terms of the sequence satisfy the recursive formula

–

To verify that this formula works for any

substitute the given explicit formula,

–

into this recursive formula.

≟

–

≟

[

–

(

–

)

–

]

–

≟

–

The formula

–

is satisfied by the sequence

–

The recursive formula is:

–

Looking for more? Try these:

Lesson: Arithmetic sequences

Lesson: Geometric sequences

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Not feeling ready yet? These can help:

U.10Convert a recursive formula to an explicit formula

Lesson: Arithmetic sequences

Lesson: Geometric sequences

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