IXL - Convert between explicit and recursive formulas (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.

–

ref_doc_title.

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

–

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.

–

⋮

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

–

and the rest of which are

–

Rewrite the terms using multiplication. (Recall that

–

⋮

Relate the expressions to the indices.

–

(

–

)

–

(

–

)

–

(

–

)

–

(

–

)

⋮

The first few terms satisfy the explicit formula

–

(

–

)

–

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

≟

–

≟

[

–

(

–

)

–

]

–

≟

–

This verifies that

–

satisfies the recursive formula

–

The explicit 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	06

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:

MM.9Convert a recursive formula to an explicit formula

MM.10Convert an explicit formula to a recursive formula

Lesson: Arithmetic sequences

Lesson: Geometric sequences

Excellent! You got that right!

Jumping to level 1 of 1

Excellent!