Last updated on Oct 24, 2026

Quadratic Sequences (Leaving Cert Mathematics): Flashcards

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Quadratic Sequences

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Definition of quadratic sequence

A sequence where the second difference is constant

General term formula for quadratic sequence

$T_n = an^2 + bn + c$

Second common difference in quadratic sequence

$2a$

First difference in quadratic sequence

Forms a linear (arithmetic) sequence

Method to find $a$ in $T_n = an^2 + bn + c$

Second difference = $2a$ , solve for $a$

Method to find $b$ and $c$ in quadratic sequence

Substitute terms, solve simultaneously

Type of sequence: 1, 3, 6, 10, ...

Quadratic sequence

Second difference of 1, 3, 6, 10, ...

$1$

Value of $a$ for sequence 1, 3, 6, 10, ...

$\frac{1}{2}$

General term $T_n$ for 1, 3, 6, 10, ...

$\frac{1}{2}n^2 + \frac{1}{2}n$

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Quadratic Sequences

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Quadratic Sequences

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Quadratic Sequences

Completed Square Form

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Quadratic Sequences

Completed Square Form

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