Preparation for Recursion

Recursion is a function which is defined with its own definition; it is defined for infinite statements for finite components. The process of repeating objects is a self-similar way is said to be recursion. Recursive formula is one of the concepts in recursion. Finding the next term of the sequence with one or more preceding terms is said to be recursive formula. Students learn recursive formula for the preparation of exam. Let us see about preparation for recursion in this article.

Worked Example Problems - Preparation for Recursion:

Example 1 for Preparation for Recursion:
The first term in a sequence is 27. Each term proceeded after first term is 8 more than the term before it. Find the recursive formula for the above sequence.
Solution:
Step 1:
Given first term `a_1 = 27`

Step 2:
Finding the next term `a_2` of the sequence
We have to add 8 to each term, we get,
`a_2 = a_1 + 8`
`a_2 = 27 + 8 = 35`

Step 3:
Finding the next term `a_3` of the sequence
We have to add 8 to each term of the sequence, we get,
`a_3 = a_2 + 8`
`a_3 = 35 + 8 = 43`

Step 4:
Then form the formula for the above sequence, we get,
`a_n = a_(n-1) + 8`
Step 5:
Therefore, the recursive formula for the sequence is `a_n = a_(n-1) + 8` .

Example 2 for Preparation for Recursion:
Write the first five terms of the sequence `a_1 = 3` and the recursive formula is `a_n = a_(n-1) + 4` .
Solution:
Step 1:
Given
The first term of the sequence is `a_1 = 3`
Recursive formula is `a_n = a_(n-1) + 4`

Step 2:
Second term:
Finding next term of the sequence using above recursive formula, we get,
`a_1 = 3`
Given formula is `a_2 = a_1 + 4`
`a_2 = 3 + 4`
`a_2 = 7`

Step 3:
Third term:
Finding next term of the sequence using above recursive formula, we get,
`a_2 = 7`
Given formula is `a_3 = a_2 + 4`
`a_3 = 7 + 4`
`a_3 = 11`

Step 4:
Fourth term:
Finding next term of the sequence using above recursive formula, we get,
`a_3 = 11`
Given formula is `a_4 = a_3 + 4`
`a_4 = 11 + 4`
`a_4 = 15`

Step 5:
Fifth term:
Finding next term of the sequence using above recursive formula, we get,
`a_4 = 15`
Given formula is `a_5 = a_4 + 4`
`a_5 = 15 + 4`
`a_5 = 19`
Therefore, the first five terms in the sequence are 3, 7, 11, 15, and 19.

My forthcoming post is on Solving System of Inequalities and cbse syllabus for class 9th will give you more understanding about Algebra.

Practice Problems - Preparation for Recursion

Problem 1:
   The first term in a sequence is 15. Each term proceeded after first term is 7 more than the term before it. Find recursive formula for the sequence.
Solution: Sequence is `a_n = a_(n-1) + 7`

Problem 2:
   Write the first five terms of the sequence `a_1 = 4` and the recursive formula is `a_n = a_(n-1) + 2` .
Solution: First five terms are 4, 6, 8, 10, and 12