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Recursive Formulas Worksheet

This worksheet focuses on understanding and applying recursive formulas for sequences, including arithmetic and geometric sequences, and solving problems involving recurrence relations.

Grade 12 Math Sequences and SeriesRecursive Formula
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Includes

3 Short AnswerMultiple ChoiceFill in the BlanksTrue / False

Standards

CCSS.MATH.CONTENT.HSF.BF.A.2CCSS.MATH.CONTENT.HSF.IF.A.3

Topics

recursive formulasequencesseriesmathematicsgrade 12
8 sections · Free to use · Printable
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Recursive Formulas

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Read each question carefully and provide your answers in the space provided. Show all your work for full credit.

1. Given the recursive formula a_n = a_(n-1) + 5, with a_1 = 3, find the first five terms of the sequence.

2. Which of the following recursive formulas represents a geometric sequence?

a

a_n = a_(n-1) + 2

b

a_n = 3 * a_(n-1)

c

a_n = a_(n-1) - n

d

a_n = (a_(n-1))^2

3. For an arithmetic sequence with a_1 = 7 and a common difference of -4, the recursive formula is a_n =   and a_1 =  .

4. Write a recursive formula for the sequence: 10, 20, 40, 80, ...

5. A recursive formula always requires the previous term(s) to find the next term.

T

True

F

False

6. A bank account starts with $1000. Each year, 5% interest is added to the balance. Write a recursive formula for the amount of money in the account at the end of 'n' years.