Question

arithematic progression​

Answer 1

In mathematics, an arithmetic progression (AP) or arithmetic sequence is a sequence of numbers such that the difference between the consecutive terms is constant. Difference here means the second minus the first. For instance, the sequence 5, 7, 9, 11, 13, 15, . . . is an arithmetic progression with common difference of 2.

If the initial term of an arithmetic progression is {\displaystyle a_{1}} a_{1} and the common difference of successive members is d, then the nth term of the sequence ( {\displaystyle a_{n}} a_{n}) is given by:

{\displaystyle \ a_{n}=a_{1}+(n-1)d} {\displaystyle \ a_{n}=a_{1}+(n-1)d},

and in general

{\displaystyle \ a_{n}=a_{m}+(n-m)d} {\displaystyle \ a_{n}=a_{m}+(n-m)d}.

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, then the members (terms) will grow towards positive infinity;

negative, then the members (terms) will grow towards negative infinity.

Answer 2

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Arithmetic Progression (AP) is a sequence of numbers in order in which the difference of any two consecutive numbers is a constant value. For example, the series of natural numbers: 1,2,3,4,5,6,… is an AP, which has a common difference between two successive terms (say 1 and 2) equal to 1 (2 -1).