Question

Detailed difference between sequence, series and Progression.

Answer 1

SequenceandSeriesare often confused because they are closely related to each other. But when we say "sequence," we are not concerned with the sum of the values of the terms, whereas in a series, we are interested in such a sum. For example:

1,1/2,1/3,1/4… uptonterms

is a sequence, and it is pretty obvious that the n(th) term will be1/n.

For every sequence, there is an associated series, and vice versa.

1+1/2+1/3+1/4+… uptonterms

So the associated series to this sequence is the series

So the basic difference is that

sequenceis a list of numbers,whereas

Seriesis the sum of numbers.

Sequencesare a set of numbers, which are arranged according to any specific rule. 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:{2, 3, 5, 7, 11, 13, 17} is a sequence. Here, rule is: Prime numbers Aseriesis a sequence of numbers that is added by + signs. The word 'series' is said torepresentthe sum of the numbers, and not the sum itself. For example:The series associated with the sequence of first 6 odd numbers is: {3+5+7+9+11+13} Progressionsare sets of numbers which are arranged according to some definite rule. The difference between a progression and a sequence is thata progression has a specific formulato calculate its nth term, whereas a sequence can be based on a logical rule like 'a group of prime numbers'. For example: {2, 4, 6, 8, 10} is a progression. Its nth term is 2n.