1. Patterns and Variables

Introduction
The branch of mathematics in which we studied numbers is arithmetic.    
In Arithmetic, numerals 1, 2, 3, 4 , -------- etc. and four fundamental operations : addition , subtraction, multiplication and division are used to deal with various problems. In Algebra, in addition to numerals, we use letters such as x, y, z in various situations to solve the problems.

Matchstick Patterns
Ram and Sarita are making patterns with matchsticks. They decide to make simple patterns of the letters of the English alphabet. Ram takes two matchsticks and forms the letter L as shown in Fig (1). Then Sarita also picks two sticks, forms another letter L and puts it next to the one made by Ram Fig (2). Then Ram adds one more L and this goes on as shown by the dots in Fig (3).

Number of matchsticks required = 2 × number of Ls. For convenience, let us write the letter n for the number of Ls. Thus, n can be any natural number 1, 2,  3, 4, 5, .... We then write, Number of matchsticks required = 2 × n. Instead of writing 2 × n, we write 2n. Note that 2n is same as 2 × n.