Question

What is the difference between sequence and progression?

Answer 1

Hint: Here we have been asked the difference between a sequence and progression. Firstly we will write the definition of both sequence and progression then we will see how the terms of both are calculated using any rule. Finally we will give some examples on how to distinguish between a sequence and a progression .

Complete answer: We have to give the difference between a sequence and a progression.
Firstly we will define both of them.
Sequences are a set of numbers that are arranged or defined according to any specific rule which mean there is something common between them.
Progressions are a set of numbers which are defined by some definite rule. It has a specific formula to find its terms.
Now the difference between both of them is that sequence is based on a logical rule or statement that is set of prime numbers or set of numbers divided by $2$ etc whereas a progression have a definite rule by which all of the element of the set are calculated example $\{2,4,6,8,10,12\}$ is a progression as the ratio between two consecutive number is $2$ and we can calculate its $n^{th}$ term by using $2n$ formula.
Let us take an example $\{2,3,5,7,11,13\}$ as we can see that it is a set of prime numbers but a definite formula to calculate the terms can’t be formed so it is not a progression but a sequence.

Note:
Sequence and progression has a very specific but can be misunderstood difference as both of them look alike. The difference is the formula to calculate the $n^{th}$ term which is present in a progression but not in a sequence. Sequences have a logical statement for the terms in it; it's not like a sequence containing random elements without having anything in common.