IXL - Convert an explicit formula to a recursive formula (Precalculus 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	2
2	3
3	4
4	5
5	6
6	7

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	3	1
3	4	1
4	5	1
5	6	1
6	7	1

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

$Confetti$

Excellent!

Now entering the Challenge Zone—are you ready?

Questions
answeredQuestions

Time
elapsedTime

hr	min	sec
00	00	04

SmartScore
out of 100
IXL's SmartScore is a dynamic measure of progress towards mastery, rather than a percentage grade. It tracks your skill level as you tackle progressively more difficult questions. Consistently answer questions correctly to reach excellence (90), or conquer the Challenge Zone to achieve mastery (100)! Learn more

Teacher tools

Work it out

Not feeling ready yet? These can help:

AA.4Find a recursive formula

Lesson: Arithmetic sequences

Lesson: Geometric sequences

Excellent! You got that right!

Jumping to level 1 of 1

Excellent!