6) In sequences, how is recursion often utilized?a) To determine the common ratiob) To define sequencesc) To find the common differenced) To calculate the explicit formula
Question
- In sequences, how is recursion often utilized?a) To determine the common ratiob) To define sequencesc) To find the common differenced) To calculate the explicit formula
Solution
b) To define sequences
Recursion is often utilized in sequences to define them. A recursive sequence, or a sequence defined by a recurrence relation, uses the terms before it to define the next term. This means that each term is a function of its previous terms. This is different from an explicit formula where each term can be calculated independently.
Similar Questions
9) What is a recurrence relation?a) A method of defining a sequence where each term is a function of the preceding termsb) A method of finding the common ratio in geometric sequencesc) A method of defining sequences independently of previous termsd) A method of solving complex problems using recursion
Instructions: For the following sequence, state the common ratio, identify which is the explicit form and which is the recursive form of the rule, and find the term listed.Sequence: 3,6,12,24…3,6,12,24…Find: a9𝑎9Common Ratio: Answer 1 Question 2an=3⋅(2)n−1𝑎𝑛=3⋅(2)𝑛−1Answer 2 Question 2an=an−1⋅2𝑎𝑛=𝑎𝑛−1⋅2a1=3𝑎1=3Answer 3 Question 2a9=𝑎9= Answer 4 Question 2
7) What does an explicit formula do?a) Represents recursive processesb) Defines the nth term based on previous termsc) Solves complex problemsd) Defines the nth term independently of previous terms
Instructions: For the following sequence, state the common difference, identify which is the explicit form and which is the recursive form of the rule, and find the term listed.Sequence: 2,202,402,602,…2,202,402,602,…Common Difference: Answer 1 Question 10
Which of the following data structures finds its use in recursion?
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