# SEQUENCE AND SERIES

SEQUENCE AND SERIES*

*Sequence.
Sequence is a list of numerical values which are related under a specific rule.

E.g 1, 2,3,4,5,6,7,8,... This is a sequence of number which is related under a specific rule which is n+1. i.e to get the next term or number we will add 1.

Examples are as follows
*2,4,6,8,10,...      (n+2)
*4, 8,16,32,...      (n*2)

In the examples here the rules are different in 1) we add 2 and in 2) we multiply 2

*A series.*
Series is the given sum of numerical values or terms which are also related with a given rules.

E.g 1+2+3+4+5+6+7+8+...
This is a series with specific rule of n+1.
Here is some examples on series
*2+4+6+8+10+...     (n+2)
* 4+8+16+32+...       (n*2)

Now note that the different between series and sequence is that sequence is just a list and series is an addition of what is on the list.

*Symbols*

Let us talk about symbols used in sequence and series.
The symbols used depends on the textbook You are using.

T or U can be used to represent Nth term. But "a" is always used to denote the first term of a series or sequence.
For first example the first term, "a" is actually 1. It is the term or value which come first in the sequence

We represent the sum of an A.P or G.P with "S". n is always used to represent the position of the term.

*A.P and G.P*

A.P means arithmetic progression
G.P means geometric progression.

An A.P can be said to be a sequence which is reducing or increasing with an additive factor called the common difference, "d".
E.g
1,2,3,4,5...           (d=1)
8,4,2,0,-2,-4,...      ( d=-2)
This are called A.P since we add or subtract a particular number to get the next term.

G.P is a sequence which is reducing or increasing with a multiplicative factor. Called the common ratio "r".
E.g
2,4,8,16,32,...        (r=2)
3,1,1/3,1/9,1/27,...  (r=1/3)

We obtain d by subtracting 1st term from the 2nd term. And we obtain r by dividing 2nd term by the 1st term.

Examples
Find the 15th term of the A.P
2,3,4,5,6...
Solution
Find the common difference.
d= 4-3=1
1st term a=2
n = 15

Substitute this in the formula and you will get it better. Consult your text book for clarification.