A sequence in numbers is an ordered list of numbers (called terms) that follow a specific pattern or rule, such as adding, subtracting, multiplying, or dividing by a certain value to get from one term to the next. For example :
- A sequence of counting numbers: 1,2, 3, 4, 5,….
- Sequence of odd numbers: 1, 3, 5, 7, 9, 11,……..
- Sequence of square numbers: 1, 4, 9, 16, 25,…….
difference between pattern and sequence
A pattern is the underlying rule or arrangement that dictates the order of items, while a sequence is the specific, ordered list of numbers or elements that follows that pattern. In other words; a pattern is the the rule(how), and a sequence is the the list of terms from the rule. in other words:
The pattern is the rule or principle governing the arrangement.
The sequence is the actual list of items that adhere to that rule.
What is a pattern?
A sequence is a list of numbers or elements arranged in a specific, connected order that follows a pattern.
In nature, pattern is the concrete, ordered set of items that results from a pattern.
A pattern can be like “add 4 to the previous number starting from 7”
The sequence would be 7, 11, 15, 19, 23, 27, 31,35,,,,,,.
Explaining sequence
A sequence is a list of numbers developed from a rule. Each number in a sequence is called a term. A sequence must come from a rule. However, a sequence can have more than one rule.
In a sequence, the terms occurs in a particular order. There is first term, second term, third term….and to infinity.
We need to establish the relationship between the value of a term and it’s position in the sequence. A position is usually represented by n. Therefore, we have 1st term, 2nd term, 3rd term,………….,n-2th term, n-1th term, nth term.
When nth term is known, any other term can be obtained using the formula developed from the rule.
consider the sequence with nth term given as 3n+2. This means the rule is that we multiply the position by 3 then add 2 to get the term in that position. To get a value for any position, we just substitute n for that position . As an example, we consider the first few positions for the sequence we defined above:
1st term: 3(1)+2 = 5
2nd term: 3(2) + 2 = 8
3rd term: 3(3) + 2 = 11
4th term: 3(4) + 2 = 14
5th term: 3(5) + 2 = 17
some commonly known sequences
- Fibonacci sequence
It is a sequence obtained by adding the first two preceding’s terms to get the next term. That is:
1, 1, 2, 3, 5, 8, 13, 21, 34, 55, 89, 144, 233, 377, 610…..
for example, the sixth term of the sequence is the sum of 3 and 5 which are the terms preceding it. similarly 9th term is the sum of 13 and 21 which are 8th and seventh term consecutively.
Arithmetic sequence
It is a sequence in which any two consecutive terms differs by the same number. The number is known as the common difference.
Geometric sequence
It is a sequence in which the ratio between any two consecutive terms is a constant value. For example 3,9,27,81,243…..
the ratio between 234 and 81 is 3. The ratio between 81 and 27 is 3 and so on.