Difference between progression and sequence
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the reminders there any difference between so tell exact which one you want
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Sequences are a set of numbers, which are arranged according to any specific rule. There is no exception for any type of numbers, any type of rules according to which they are arranged. The set of numbers should have a definite, logical rule according to which they are arranged. It need not be a mathematical formula, but it should be logical. Such a set of numbers are called a sequence of numbers.
For example, the following is a sequence of numbers, because they are arranged according to a definite rule:
{2, 4, 6, 8, 10, 12} Rule: nth term = 2n
The following is a sequence of odd numbers:
{3, 5, 7, 9, 11, 13} Rule: nth term = 2n + 1
The following is also a sequence of numbers, as they too have a logical rule:
{2, 3, 5, 7, 11, 13, 17} Rule: Prime numbers
Progressions are yet another type of number sets which are arranged according to some definite rule. The difference between a progression and a sequence is that a progression has a specific formula to calculate its nth term, whereas a sequence can be based on a logical rule like 'a group of prime numbers', which does not have a formula associated with it.
Now you may be wondering that a set of prime numbers should a progression because we can predict its nth term, but a progression needs a specifically stated formula, and, it is to be noted that prime numbers cannot be predicted with the help of any formula; Till date, the formula for the nth prime number has not be found. This means that we can only calculate the nth prime number with the method of selecting each successive number and checking whether it is prime or not.
Therefore {2, 4, 6, 8, 10, 12} represents a progression where the nth term is given by '2n', and, on the other hand, {2, 3, 5, 7, 11, 13, 17} represents a sequence that is not a progression, because although it is based on a definite logical rule (prime numbers), but there is no formula to calculate its nth term.
For example, the following is a sequence of numbers, because they are arranged according to a definite rule:
{2, 4, 6, 8, 10, 12} Rule: nth term = 2n
The following is a sequence of odd numbers:
{3, 5, 7, 9, 11, 13} Rule: nth term = 2n + 1
The following is also a sequence of numbers, as they too have a logical rule:
{2, 3, 5, 7, 11, 13, 17} Rule: Prime numbers
Progressions are yet another type of number sets which are arranged according to some definite rule. The difference between a progression and a sequence is that a progression has a specific formula to calculate its nth term, whereas a sequence can be based on a logical rule like 'a group of prime numbers', which does not have a formula associated with it.
Now you may be wondering that a set of prime numbers should a progression because we can predict its nth term, but a progression needs a specifically stated formula, and, it is to be noted that prime numbers cannot be predicted with the help of any formula; Till date, the formula for the nth prime number has not be found. This means that we can only calculate the nth prime number with the method of selecting each successive number and checking whether it is prime or not.
Therefore {2, 4, 6, 8, 10, 12} represents a progression where the nth term is given by '2n', and, on the other hand, {2, 3, 5, 7, 11, 13, 17} represents a sequence that is not a progression, because although it is based on a definite logical rule (prime numbers), but there is no formula to calculate its nth term.
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