Write a recursive definition for the sequence 11, 8, 5, 2

Solution:

The recursive process involves an application of a rule to successive results.

The above sequence is obtained from the rule which is applied recursively and is stated as follows:

The n^th term is obtained by subtracting 3 from the (n - 1)^th term or in other words the (n + 1)^th term is obtained from the n^th term by subtracting 3.

Mathematically it can be stated as:

a_n= a_n-1 - 3

Or

a_n+1= a_n - 3

We take another example of a sequence depicting a recursive relationship.

1, 3, 7, 15, 31

The above sequence is defined by a recursive relation:

a_n =2_n-1 + 1

Or

a_n+1 =2_n + 1

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Write a recursive definition for the sequence 11, 8, 5, 2

Summary

The recursive definition for the sequence 11, 8, 5, 2 is \(a_{n}= a_{n-1} - 3\).