In mathematics, summing up numbers is important. We can do that with the help of a calculator when the numbers are small. But if the numbers are large, we need some formula to arrive fast at the answer.
Key Takeaways
- A sequence refers to an ordered list of numbers, whereas a series consists of the sum of the terms in a sequence.
- Sequences can be finite or infinite, but series always have a sum, either finite or infinite.
- Both sequences and series can follow arithmetic, geometric, or other patterns, determining their properties and behavior.
Sequence vs Series
In mathematics, a sequence refers to a series of numbers that follow a particular order. It follows a pattern and can be used to solve specific problems. A series is a set of numbers that is split up by a plus symbol. A series does not follow an ordered list or pattern.
Sequence is a term used in mathematics to determine the order of numbers. They will have a series of numbers, and these numbers will always follow an order.
A series is a set of numbers, and these numbers will be split with the help of a plus symbol. This is very important because it helps us to sum the numbers with the help of a simple formula.
Comparison Table
| Parameters of Comparison | Sequence | Series |
|---|---|---|
| Definition | They are set of numbers in an ordered list | They are set of numbers having plus symbol in between |
| Main difference | They don’t have any symbol in between | They are different because of the plus symbol |
| Order Importance | Order is very important | Order is not much important |
| Pattern | They follow a specific pattern | They don’t have any specifics. They will sum up |
| Order Sequence | The order sequence will be different | It is the same in all the cases |
What is Sequence?
A sequence is a series of numbers in an ordered list. This is a specific pattern or function that is followed in mathematics.
It is an important topic that is studied by students in mathematics. Based on this, they used to solve some specific problems as well. There is a formula that is used to calculate the sequence.
The sequence will always follow a pattern. And it will always follow the order as well. To first calculate, you need to have the formula in hand.
What is Series?
A series is used in mathematics, and they contain a set of numbers. But here, the numbers will be split up by the plus symbol. And these numbers will not follow any order.
This can be calculated by using some special formula. Because the number length might be large and we can’t keep on adding the numbers till we reach the last number.
The terms used in series can either be real or complex numbers. But there will be generality that is always possible. Common series is also one of its types, and it is mainly used for solving consecutive numbers.
Main Differences Between Sequence and Series
- A sequence will follow a specific pattern. On the other hand, a series will not follow any pattern.
- In sequence, the order sequence will be different. But in series, the order sequence will be the same in all the cases.
- https://psycnet.apa.org/record/1962-06964-001
- https://link.springer.com/content/pdf/10.1007/978-3-319-45686-7.pdf
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