Recursive Formula in Arithmetic Sequences
Recursion is the process of choosing a starting term and repeatedly applying the
same process to each term to arrive at the following term. Recursion requires that you
know the value of the term immediately before the term you are trying to find.
A recursive formula always has two parts:
1. the starting value for a1.
2. the recursion equation for an as a function of an-1 (the term before it.)
Recursive formula:
Same recursive formula:
Examples:
1. Write the first four terms of the sequence:
In recursive formulas, each term is used to produce the next
term. Follow the movement of the terms through the set up
at the left.
Answer: -4, 1, 6, 11
2. Consider the sequence 2, 4, 6, 8, 10, ...
Explicit formula:
Recursive formula:
Certain sequences, such as this arithmetic
sequence, can be represented in more than one
manner. This sequence can be represented as
either an explicit (general) formula or a recursive
formula.
3. Consider the sequence 3, 9, 27, 81, ...
Explicit formula:
Recursive formula:
Certain sequences, such as this geometric
sequence, can be represented in more than one
manner. This sequence can be represented as
either an explicit formula or a recursive formula.
