Sequences and Series

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Sequence is a set of things 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. Sum of first p terms in of a sequence is
Here i is the index of summation
1 is the lower limit and
P is the upper limit
Series is a number of things or events of similar type coming one after another.
Example: A, AA, AAA,……
There are different types of sequences or progressions.
  • Arithmetic Progression
  • Geometric Progression
  • Harmonic Progression
A X H = G²
Here A stands for Arithmetic mean
H stands for Harmonic mean and
G stands for Geometric mean
1) Fourth and tenth terms in a arithmetic sequence are 48 and 36 respectively. Find the general term of the sequence.
Answer:
General term of Arithmetic sequence is tn = a + (n-1)d
For fourth term n= 4
t4 = a + (4-1)d
48 = a+3d
a = 48 – 3d
For tenth term n = 10
t10 = a + (10-1)d
36 = a + 9d
Substitute a = 48 – 3d in 36 = a+ 9d
36 = 48 – 3d + 9d
36 = 48 + 6d
6d = -12
d = -2
Substitute d = -2 in 48 = a+3d
48 = a + 3(-2)
48 = a -6
a = 54
General term t_n = 54 + (n-1)-2
tn = 54 -2n +2
tn = 56 – 2n

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