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Recursive and Explicit Formulas Worksheet

This worksheet focuses on understanding and applying recursive and explicit formulas for sequences, suitable for Grade 12 mathematics students.

Grade 12 Math Sequences and SeriesRecursive and Explicit Formulas
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Includes

2 Short AnswerFill in the BlanksMultiple ChoiceTrue / FalseLong Answer

Standards

CCSS.MATH.CONTENT.HSF.BF.A.1.ACCSS.MATH.CONTENT.HSF.BF.A.2

Topics

sequencesseriesrecursiveexplicitformulasgrade 12math
8 sections · Free to use · Printable
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Recursive and Explicit Formulas

Name:

Date:

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Read each question carefully and provide the requested information. Show all your work for full credit.

1. Explain the key difference between a recursive formula and an explicit formula for a sequence.

2. For the sequence 3, 7, 11, 15, ..., the common difference is  .

3. A recursive formula for an arithmetic sequence requires the first term and the  .

4. An explicit formula allows you to find any term directly without knowing the   terms.

5. Which of the following is an explicit formula for the sequence 2, 4, 8, 16, ...?

a

a_n = a_(n-1) * 2

b

a_n = 2n

c

a_n = 2^n

d

a_n = n + 2

6. Write a recursive formula for the arithmetic sequence where a_1 = 5 and the common difference is 3.

7. Write an explicit formula for the geometric sequence where a_1 = 4 and the common ratio is 0.5.

8. The sequence defined by a_n = 2n + 1 is an arithmetic sequence.

T

True

F

False

9. A population of bacteria doubles every hour. If you start with 100 bacteria, write both a recursive and an explicit formula to model the population after 'n' hours. Then, use the explicit formula to find the population after 5 hours.