IXL - Write a formula for a recursive sequence: function notation (Algebra 1 practice)

Which recursive formula can be used to define this sequence for

2, 8, 14, 20, 26, 32, ...

(

)

(

–

)

(

)

(

–

)

(

)

(

–

)

(

–

)

(

)

(

–

)

ref_doc_title.

Learn with an example

question

Which recursive formula can be used to define this sequence for

–

5, 19, 33, 47, 61, ...

(

)

(

–

)

(

)

(

–

)

–

(

)

–

(

–

)

(

)

–

(

–

)

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 variable

of the term

(

)

is called the

index.

A recursive formula defines a sequence using earlier terms.

solution

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

n	f ( n )	f ( n ) – f ( n – 1 )
1	– 9	undefined
2	5	14
3	19	14
4	33	14
5	47	14
6	61	14

The table shows that

(

)

–

(

–

)

for

Since the difference between consecutive terms is always the same, this sequence is

arithmetic.

Write this rule as a recursive formula.

(

)

–

(

–

)

(

)

(

–

)

Since the first term in the sequence is

(

)

the term

(

–

)

is not defined for

≤

So, this formula is only valid for

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:

U.6Identify a sequence as explicit or recursive

Evaluate recursive formulas for sequences: function notation

Lesson: Arithmetic sequences

Lesson: Geometric sequences

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