Question

what is arithmetic progression? define its formula also.

Answer 1

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 {\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}.

Answer 2

arthametic progression -common ratios are equal. tn=a+n-1)d