A sequence is a set thing in a certain order
Example: 2, 4, 6… (Sequence of even numbers)
A sequence contains list of values in an ordered way. All these values are called as terms.
A finite sequence is that which contains a finite number of terms.
a_{1}, a_{2}, ……………………………,a_{n} ( n is some finite value)
An infinite sequence is that which contains an infinite number of terms.
a_{1}, a_{2}, ……………………………,a_{n}, ……………… ( n is an infinite number)
Different types of sequences are

Arithmetic sequence or progression (A.P)
d Common difference
A.P is of the form a, a+d, a+2d .......
l Last term
Last term = t
_{n} = a + (n1) d
a First term
Sum of n terms = 2a + (n1)d or a + l
n number of terms

Geometric sequence (G.P) r common ratio
G.P is of the form a, ar, ar².....
Last term = t_{n} = ar^{(n1)}

Harmonic sequence (H.P)
H.P is of the foxrm ^{1}⁄_{a }, ^{1}⁄_{(a+d)} ,^{ 1}⁄_{(a+2d)},…………
t_{n} =^{ 1}⁄_{(nth term of corresponding A.P)}
Harmonic mean of two terms a and b is ^{2ab}⁄_{(a+b)}.
A X H = G²
Here A stands for Arithmetic mean
H stands for Harmonic mean and
G stands for Geometric mean
Example:
Find the first three terms of the sequence t_{n} = (2)^{n}/( n+1)
Answer:
First term = n = 1
t_{1} = (2)^{1}/( 1+1) = (2)/( 2) = 1
Second term = n = 2
t_{2} = (2)^{2}/( 2+1) = 4/( 3)
Third term = n = 3
t_{3} = (2)^{3}/( 3+1) = (8)/( 4) = 2
The first three terms are 1, 4/3, 2