Factual Questions 

1.What is a  sequences?

A sequence is a list of numbers arranged according to a rule and is separated by commas is known as sequences.

For example; 1,2,3,4,5,

2. What is a series ?

The sum of terms of a sequence is series.

For example; 1+2+3+4……

There are different types of  series ; Arithmetic series, geometric series, convergent series and divergent series.

Arithmetic Series : A types of series which involves addition or subtraction of  a sequence in a sequence is known as     arithmetic series.For example; 1+2+3+4…….1000000. The first term is and the constant difference is d and the number of terms is n.

Geometric series: A series which involves division or multiplication is known as geometric sequence.It has a constant ratio between terms. For example; 2+6+18+54. The first term is a¡ and the common ratio is r and the number of term is n.

Convergent Series: A series in which there is a limit to the partial sum. For example; 0.9,0.09.0.009,0.0009,…….1. The series converges to 1.

Divergent Series: A series which has no limit. It does not diverge . For example:1, 1+2, 1+2+3, 1+2+3+4,…..

 

3.How can we distinguish between and analyse different types of sequences and series?

Series is a sum of terms which can be arithmetic or geometric. Series are always infinite.If the series have  a constant term its means that its is arithmetic. Where if it has constant ratio it means it is geometric sequence.

  1. tco
    Oct 01, 2018

    Hi Aaliya,

    You clearly define sequence and series and the different types in your answers to the first two questions.

    But in the third question 1, 4, 9, 16 is a sequence because it is a list of numbers. 3+7+11+15+… is a series because we are adding terms. You haven’t really answered the question.

    I’d like you to think about the third question as two separate ones:
    a) How can we distinguish between different types of S&Ss?
    b) How do we analyze different different types of S&Ss?

    Then I’ll also add … why do we analyze S&Ss?

    Reply