UNIT OVERVIEW

In Grade 10, you studied arithmetic sequences where the difference between consecutive terms stays constant. Now you will explore quadratic sequences, where the first differences change, but those changes follow a predictable pattern.

In this unit, you will learn to:

• Identify quadratic sequences by finding constant second differences
• Calculate first and second differences of any sequence
• Derive the general term $T_n = an^2 + bn + c$ for quadratic sequences
• Use the second difference to find the value of $a$
• Solve for $b$ and $c$ using simultaneous equations
• Work backwards from the general term to generate sequences
• Solve problems involving unknown terms in quadratic sequences
• Apply quadratic sequences to real-world problems

Where quadratic sequences appear in life:

1. Stacking objects: When you stack cans in a triangular display, the total number of items forms a quadratic sequence.

2. Falling objects: The distance an object falls each second increases following a quadratic pattern due to gravity.

3. Seating arrangements: Stadium rows often have more seats as you move outward. The total seats up to row $n$ can follow a quadratic sequence.

4. Triangular numbers: The sequence $1, 3, 6, 10, 15, ...$ (dots arranged in triangles) is quadratic.

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