Introduction to patterns and functions math:
The various number patterns in mathematics are formed by the functions that define the relation between the consecutive numbers in the series. If the interval between the numbers remains same through the series then the series is called as recursive series. In the following article we will see in detail about the topic recursion and special sequences online study.
More about Patterns and Functions Math:
Recursion:
The recursive series is not just a single series but there are various series that can be formed by the repetition of the condition that defines the numbers in the series. In the recursive series they may be formed by the repeating interval or the repeating conditions that defines the consecutive numbers of the series. All the recursive series requires two important parameters, the first value of the series and the rule or the condition that defines the occurrence of the numbers in the series.
Fibonacci numbers:
The Fibonacci series starts with two numbers and the rest of the numbers in the series are formed by the rule that the numbers in the series are the sum of the previous two Fibonacci numbers. The function used to form the numbers in the Fibonacci series is given by,
`F_n = F_(n-1) + F_(n-2)`
Polygonal numbers:
The polygonal numbers are the numbers which are represented as dots and arranged in the form of a particular polygon. And all the polygons have such kind of number sequences. All the polygonal numbers starts with 1 and the next numbers in the series is calculated by increasing one dot in consecutive arms of the polygonal shape and filling the rest of the arms.
Example Problem on Patterns and Functions Math:
1. Find the first five numbers in the recursive series with the first number `a_0 = 10` and `a_(n+1) = a_n +3` .
Solution:
`a_0` = 10
`a_1` = `a_0` + 3 = 10+3 = 13
`a_2` = `a_1` + 3 = 13+3 = 16
`a_3` = `a_2` + 3 = 16+3 = 19
`a_4` = `a_3` + 3 = 19+3 = 22
Practice problem on patterns and functions math:
1. Find the first 6 numbers in the recursive series with `a_0 = 20` and `a_(n+1) = (a_n)-(2*n)+3` .
Answer: 20, 21, 20, 17, 12, 5.
The various number patterns in mathematics are formed by the functions that define the relation between the consecutive numbers in the series. If the interval between the numbers remains same through the series then the series is called as recursive series. In the following article we will see in detail about the topic recursion and special sequences online study.
More about Patterns and Functions Math:
Recursion:
The recursive series is not just a single series but there are various series that can be formed by the repetition of the condition that defines the numbers in the series. In the recursive series they may be formed by the repeating interval or the repeating conditions that defines the consecutive numbers of the series. All the recursive series requires two important parameters, the first value of the series and the rule or the condition that defines the occurrence of the numbers in the series.
Fibonacci numbers:
The Fibonacci series starts with two numbers and the rest of the numbers in the series are formed by the rule that the numbers in the series are the sum of the previous two Fibonacci numbers. The function used to form the numbers in the Fibonacci series is given by,
`F_n = F_(n-1) + F_(n-2)`
Polygonal numbers:
The polygonal numbers are the numbers which are represented as dots and arranged in the form of a particular polygon. And all the polygons have such kind of number sequences. All the polygonal numbers starts with 1 and the next numbers in the series is calculated by increasing one dot in consecutive arms of the polygonal shape and filling the rest of the arms.
Example Problem on Patterns and Functions Math:
1. Find the first five numbers in the recursive series with the first number `a_0 = 10` and `a_(n+1) = a_n +3` .
Solution:
`a_0` = 10
`a_1` = `a_0` + 3 = 10+3 = 13
`a_2` = `a_1` + 3 = 13+3 = 16
`a_3` = `a_2` + 3 = 16+3 = 19
`a_4` = `a_3` + 3 = 19+3 = 22
Practice problem on patterns and functions math:
1. Find the first 6 numbers in the recursive series with `a_0 = 20` and `a_(n+1) = (a_n)-(2*n)+3` .
Answer: 20, 21, 20, 17, 12, 5.
No comments:
Post a Comment