Question

in arithmetic progression what is the difference between an and n​

Answer 1

Answer:

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

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

and in general

{\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

Answer:

nth Term of an AP. The nth term of an arithmetic progression whose first term is a1 and whose common difference is d is given by an = a1 + (n – 1) d.

Step-by-step explanation:

An arithmetic progression is a sequence where each term is a certain number larger than the previous term. ... The nth term of this sequence is 2n + 1 . In general, the nth term of an arithmetic progression, with first term a and common difference d, is: a + (n - 1)d . So for the sequence 3, 5, 7, 9, ...