Question

arithmetic progression in which part

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. 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 a 1 {\displaystyle a_{1}} a_{1} and the common difference of successive members is d, then the nth term of the sequence ( a n {\displaystyle a_{n}} a_{n}) is given by:

a n = a 1 + ( n − 1 ) d {\displaystyle \ a_{n}=a_{1}+(n-1)d} {\displaystyle \ a_{n}=a_{1}+(n-1)d},
and in general

a n = a m + ( n − m ) d {\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.
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