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# Basic Arithmetic

Arithmetic:
Branch of mathematics which deals with numerical aspects of numbers and which involves the study of the skills necessary to manipulate numbers. In arithmetic. we understand the structure of the number system. It facilitates to change the numbers from one form to another. For example, the numbers in the form of the fraction can be changed to decimal forms.

Arithmetic Means (AM) :
The terms of an arithmetic progression, lying between the first and the last are called arithmetic means of the first and the last terms. To insert n means between two numbers a and b implies having n+2
numbers in arithmetic progression with common difference d are equal to b-a/n+1. Thus, the n arithmetic means in between a and b are a+[b-a/n+1], a+2[b-a/n+1],โฆ..a+n[b-a/n+1]. The arithmetic mean of a and b is taken as (a+b) is divisible by 2.

The arithmetic mean of n different quantities,

a_1,a_2,a_3โฆโฆ.a_n, is (a_1+a_2, +โฆโฆ. +a_n) divided by n

Arithmetic Progression or sequence (A.P):

A sequence in which the difference between any two
consecutive terms are constant. The constant difference is called the common difference. If a is the term and d the common difference of an A.P. then its nth term is equal to a+(n-1)d and sum of its n terms, Sn is given by

Sn=[n/2]{2a+(n-1)d}

Arithmetic Series :
A series formed with the terms of an arithmetic progression. For example, the series 3+6+9+12+15+.. is an arithmetic series with the first term is 3 and
the common difference is 3.

Arithmetico- Geometric Series:
A series whose rth term is the product of the th term of an A.P and the rth term of a G.P. The rth term is [a+(r-1)d] x^r-1. If Sn denotes the sum of its first n terms, then
Sn=a+ (a + d)x + (a +2d) x+โฆ+[a +(n-1) d] x^n-1

Arithmetic meaning in urdu ilm ul hissab ุนูู ุญุณุงุจ means it’s knowledge of mathematics.