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It is defined as a set of numbers specified in a particular order by
some assigned law.
For example, S1 = 2, 3, 5, 7 and S2 = 1, 4, 7, 10, 13
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is a |
| sequence of numbers where each term is three more than the
previous term. |
Almost in all the sequence a general term can be written which
represents the terms of the sequence. For example, the general term for
the sequence of consecutive odd numbers starting from 1 will be, 2n – 1,
where n can take any value from 1 to infinity. Similarly the general term
for the sequence of consecutive even numbers starting from 2 can be
represented as 2n in principle, the general term of any sequence can be
found by taking the difference between the sum of first n terms and (n –
1) terms of the sequence.
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the sum of first n terms, |
Series
When a sequence is represented in summation form it is called a series
and the summation is represented by the symbol ‘ Σ ’.
For example, 1 + 3 + 5 + 7 + 9 is a series of first five odd numbers
and is represented as,
A sequence is called an Arithmetic Progression (A.P.) if the
differences between any two pairs of consecutive terms are same. This
constant difference is called the common difference (d). The first term is
denoted
For example, 2, 4, 6, 8, 10 or 1, 4, 7, 10, 13.
In the first one the common difference is 2 and in the second the
common difference is 3.
Let the first term of an AP be ‘a’ and the common difference is ‘d’,
then the terms of the AP can be written as: a, a + d, a + 2d, a + 3d...
The n term, an, is generalized as, an = a + (n – 1) d.
A sequence is called a geometric progression (G.P.) if the ratio of any
term to the preceding term is a constant, called common ratio. If the
first term is 'a' and the common ratio is 'r', then the sequence takes the
form a, ar,
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