# Sequences and Series

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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.
a1, a2, ……………………………,an ( n is some finite value)
An infinite sequence is that which contains an  infinite number of terms.
a1, a2, ……………………………,an, ……………… ( 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 = tn = a + (n-1) d    a First term
Sum of n terms = 2a + (n-1)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 = tn = ar(n-1) • Harmonic sequence (H.P)
H.P is of the foxrm 1a , 1(a+d) , 1(a+2d),…………
tn = 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 tn = (-2)n/( n+1)