Polynomials | Class 9 Mathematics Notes

2.3 EXPLORING LINEAR PATTERNS

This section explores linear patterns through sequences generated by algebraic expressions. Using a growing pattern of square tiles, where each stage adds two more tiles than the previous, the number of tiles at stage n is expressed as 2n - 1, a linear polynomial of degree 1. The constant difference between consecutive terms (2) characterizes the linear pattern. The section includes tables illustrating the number of tiles at various stages and the amount left in a spending scenario modeled by a linear expression. Another example models auto-rickshaw fare with a fixed initial cost and incremental cost per km after the first 2 km, leading to a piecewise linear function. The section emphasizes that linear patterns have constant differences between terms and introduces the concept of linear growth and decay. Students are encouraged to predict terms in sequences and solve real-life problems using linear expressions.

📊 Diagram: Fig. 2.4: A growing pattern of square tiles

🧪 Activity: Think and Reflect questions ask students to predict terms in sequences and solve for unknowns using linear expressions.

🔗 Connection: Leads to the study of linear growth and decay functions in the next section.

Table on page 7 (2×8)

Table on page 7 (2×6)

Table on page 8 (2×7)