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)
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
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Arithmetic sequence or progression (A.P) d
Common differenceA.P is of the form a, a+d, a+2d ....... l Last termLast term = tn = a + (n-1) d a First termSum 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)
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Harmonic sequence (H.P)
H.P is of the foxrm 1⁄a , 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 = G²Here A stands for Arithmetic meanH stands for Harmonic mean andG stands for Geometric mean
Example:
Find the first three terms of the sequence tn = (-2)n/( n+1)
Answer:
First term = n = 1
t1 = (-2)1/( 1+1) = (-2)/( 2) = -1
Second term = n = 2
t2 = (-2)2/( 2+1) = 4/( 3)
Third term = n = 3
t3 = (-2)3/( 3+1) = (-8)/( 4) = -2
The first three terms are -1, 4/3, -2
First term = n = 1
t1 = (-2)1/( 1+1) = (-2)/( 2) = -1
Second term = n = 2
t2 = (-2)2/( 2+1) = 4/( 3)
Third term = n = 3
t3 = (-2)3/( 3+1) = (-8)/( 4) = -2
The first three terms are -1, 4/3, -2
