Recursive and Explicit Formulas Worksheet
This worksheet focuses on understanding and applying recursive and explicit formulas for sequences, suitable for Grade 12 mathematics students.
Includes
Standards
Topics
Recursive and Explicit Formulas
Name:
Date:
Score:
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_n = a_(n-1) * 2
a_n = 2n
a_n = 2^n
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.
True
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.
Related Worksheets
Fibonacci Sequence Exploration
This worksheet explores the properties and applications of the Fibonacci sequence, suitable for Grade 12 students.
Grade 12 Arithmetic Series Worksheet
A comprehensive worksheet for Grade 12 students to practice and master arithmetic series concepts, including finding terms, sums, and solving related problems.
Grade 12 Math: Geometric Sequences Worksheet
This worksheet focuses on understanding, identifying, and applying the properties of geometric sequences for Grade 12 students.
Grade 12 Math: Geometric Sequences Worksheet
This worksheet focuses on understanding, identifying, and applying the properties of geometric sequences for Grade 12 students.
Grade 12 Arithmetic Sequences Word Problems
This worksheet focuses on applying the concepts of arithmetic sequences to solve real-world word problems, suitable for Grade 12 students.
Graphing Sequences Worksheet
Grade 12 Math worksheet focusing on graphing arithmetic and geometric sequences, identifying patterns, and interpreting graphs of sequences.
Geometric Series Worksheet
A Grade 12 math worksheet focusing on understanding and applying the concepts of geometric series, including finite and infinite series, common ratio, and sum formulas.
Fibonacci Numbers Exploration
A Grade 12 math worksheet exploring the properties and applications of Fibonacci numbers, including the Golden Ratio and recurrence relations.