Arithmetic Progression
Arithmetic Progression
In mathematics, an arithmetic progression (AP) or arithmetic sequence is a sequence of numbers such
that the difference between the consecutive terms is constant. For instance, the sequence 3, 5, 7, 9, 11,
13, ... is an arithmetic progression with common difference of 2.
If the initial term of an arithmetic progression is and the common difference of successive members is
d, then the nth term of the sequence () is given by:
A finite portion of an arithmetic progression is called a finite arithmetic progression and sometimes just
called an arithmetic progression. The sum of a finite arithmetic progression is called an arithmetic
series.
The behavior of the arithmetic progression depends on the common difference d. If the common
difference is:
>> Positive, the members (terms) will grow towards positive infinity.
>> Negative, the members (terms) will grow towards negative infinity.
Know More About :- Harmonic Progression


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Arithmetic progression is a sequence in mathematics that progresses in such a way that the difference
between two consecutive numbers is constant and the constant difference is given by (d).
It can be explained as (p1) is the initial term of the successive series and (d) is the difference between
them then the nth term is given by the arithmetic progression (pn) = p1 + (n - 1)d. And in general (pn)
= pm + (n - m) d, Where (d) can be given as d = p2 - p1, that means`d' is the difference of the second
term and the previous term.
If this sequence of series is finite to any portion then this series is called as finite arithmetic
progressions or some time just arithmetical progression. The sum of the terms of the finite arithmetic
progression is also known as the arithmetic series, where all the terms of the series are added.
Here the overall nature of arithmetic progression depends on the common difference (d) and the
common difference is: If positive then the members or the terms will grow in the positive infinite. If
negative then the members of the terms will grow in the negative infinite.
In arithmetic progression we can perform various mathematical operations on these series like sum,
product etc. The SUM of the arithmetic progression terms can be given as:
Qn = p1 + (p-1 + d) + (p1 + 2d) + ........... + (p1 + (n - 2) d) + (p1 + (n - 1) d),
Qn = (pn - (n - 1) d) + (pn - (n - 2)d) + ........... + ( pn - 2d) + (pn - d) + pn.
Here adding these two series will cancel all the terms of (d) and provides us, 2Qn = n (p1 + pn). And
dividing both sides with 2 will produce a common equation as:- Qn = n/2 ( p1 + pn).
Read More About :- Linear Equations in Two Variables


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