Difference Between Sequence and Series (With Table)

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. There are two most commonly used methods called Sequence, and the next method is Series which is used by students for many exams to arrive at the answer. 

Sequence vs Series

The difference between Sequence and Series is that in the sequence, you will be able to find ghat the numbers are following the certain, and they have some specific pattern to be followed. A Series will have a set of numbers by having a plus symbol which will sum up the numbers at the end, and they don’t have any specific pattern to be followed.

The 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. There are even diagrams available to solve the problems of sequence. With diagrams on your side, you will be able to understand the problem well and can arrive at the answer even faster than you have anticipated.

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. This will be very useful in competitive exams because there we have to sum up many numbers and we can’t waste our time by adding them one by one. 

Comparison Table Between Sequence and Series

Parameters of ComparisonSequenceSeries
DefinitionThey are set of numbers in an ordered listThey are set of numbers having plus symbol in between
Main differenceThey don’t have any symbol in betweenThey are different because of the plus symbol
Order ImportanceOrder is very importantOrder is not much important
PatternThey follow a specific patternThey don’t have any specifics. They will sum up
Order SequenceThe order sequence will be differentIt 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 a function that is followed in mathematics. There are two types of sequences available in maths. And they are either an infinite sequence or finite sequence. This method follows the order of succession. Wherever you see the sequence, they will follow some specific order.

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. There are 4 types of sequence available in mathematics, and they are arithmetic, geometric, harmonic, and Fibonacci. The sequence will denote the position of a number. You can even define the sequence based on its types. We can determine whether the series is finite or infinite by determining whether the sequence is finite or infinite.

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. Once you substitute all the values in the formula, you will get an answer to that. It can be done by following some examples instead of jumping into the question straight away without understanding it properly.

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 plus symbol. And these numbers will not follow any order. When you sum up these numbers, they will give some value. The plus sign here will mainly indicate that you should add them up to get the answer. In mathematics, it is mainly given as the cumulative sum.

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. It will be a headache, and it will consume a lot of our time. And the better way to do this is by following the formula listed so that we can solve the problem within seconds or minutes. Because that entirely depends on the length of the numbers.

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. But you can’t always expect them to be in a certain order. For calculating, all that matters is you should have to know the first and the last number so that you can substitute these terms in the formula, which will eventually give you the answer to the question.

Main Differences Between Sequence and Series

  1. A sequence is a set of numbers having following an ordered list. On the other hand, a series is a set of numbers that having a plus symbol in between.
  2. A sequence will always follow an order. On the other hand, a series will not follow any specific order.
  3. A sequence will not have any arithmetic symbol between them. But a series will have plus symbol in between them, to sum up the numbers.
  4. A sequence will follow a specific pattern. On the other hand, a series will not follow any pattern.
  5. In sequence, the order sequence will be different. But in series, the order sequence will be the same in all the cases.

Conclusion

Both these methods are used in mathematics, and they are famous as well. Because it will help you to arrive at the answer, imagine if we want to add up all the numbers in a series, then it is going to consume all our time. If we can do that with the help of a formula, it will help us to arrive at the answer very fast.

Learning this method will help us in solving some complex mathematical problems that are asked in competitive exams and some other exams as well. It is taught to school students so that they can get a clear idea at the school level itself. The best way to learn and practice this method is by practising more sums and saving the example sums. 

References

  1. https://psycnet.apa.org/record/1962-06964-001
  2. https://link.springer.com/content/pdf/10.1007/978-3-319-45686-7.pdf
x
2D vs 3D