nth Term of Quadratic Sequences Flashcards

GCSE Mathematics (Edexcel) 1MA1

Quadratic sequence

A sequence where the difference between consecutive terms changes, forming a second difference that is constant.

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Quadratic sequence

A sequence where the difference between consecutive terms changes, forming a second difference that is constant.

Second difference

The difference between consecutive first differences in a sequence. A constant second difference indicates a quadratic sequence.

General form of nth term for quadratic sequence

The nth term of a quadratic sequence is in the form an² + bn + c.

Step 1 to find nth term of quadratic sequence

Find the first differences between consecutive terms of the sequence.

Step 2 to find nth term of quadratic sequence

Find the second differences between consecutive first differences. Confirm it is constant.

Step 3 to find nth term of quadratic sequence

Divide the constant second difference by 2 to find the coefficient 'a' in an².

Step 4 to find nth term of quadratic sequence

Subtract an² from each term in the sequence to form a new linear sequence.

Step 5 to find nth term of quadratic sequence

Find the nth term of the new linear sequence (bn + c).

Step 6 to find nth term of quadratic sequence

Combine an² and the nth term of the linear sequence to form the full nth term.

Example of quadratic sequence

For the sequence 2, 6, 12, 20, 30, the nth term is 2n² - n.

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