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11 Introduction to Algebra

By observing a given pattern and generalizing, we can get the subsequent term(s).
Let’s understand how patterns are generalized with the help of the following example:
Rafiq wants to buy pens. The cost of a pen is ` 6. To buy Number of
two pens he needs 6 × 2 = ` 12, whereas to buy three pens Cost in rupees
pens he needs 6 × 3 = ` 18 and so on. Clearly, the amount 1 1 × 6 = 6
increases as the number of pens increases. We can see a 2 2 × 6 = 12
pattern in the table given alongside and generalize it to find 3 3 × 6 = 18
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the subsequent terms as follows:
Total amount required = Cost of 1 pen × Number of pens = 6n, where n represents the number
of pens. Since the value of n is not fixed, it is called a variable. The expression 6n is the general
expression for the cost of n pens, given the cost of one pen is ` 6.
In this lesson, we shall begin with the study of a new branch of Do you know?
Mathematics, i.e., Algebra. In Algebra we use numerals, signs of The word algebra is derived
basic operations in Mathematics (addition, subtraction, multiplication from the title of the book
and division) and letters of English or Greek alphabet. These letters ‘Aljebar w’al almugabalah’.
are used to represent some unknown terms or to generalize a result.
Use of letters allows us to form rules and formulae in general.

Matchstick Patterns
1. Sameer decides to make patterns of squares using matchsticks as shown below:

Number of squares 1 2 3 4 5 6 7 ... ...
Number of matchsticks used 4 7 10 13 16 19 22 ... ...
Sameer observed that the number of matchsticks used = 3 (Number of squares) + 1
= 3 × n + 1 = 3n + 1
2. Sarita and Savera were making patterns of triangles using matchsticks as shown below:

Number of triangles 1 2 3 4 5 … …
Number of matchsticks 3 6 9 12 15 … …

Sarita and Savera observed that the number of matchsticks used = 3 (Number of triangles)
= 3n