Patterns and Sequences (Leaving Cert Mathematics): Quizzes

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Quadratic Sequences
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What is the highest power in the nth term of a quadratic sequence?

n2n^2

What is the general form of a quadratic sequence?

Tn=an2+bn+cT_n = an^2 + bn + c

What key feature identifies a quadratic sequence?

Constant second differences

How is the coefficient of n2n^2 related to the second difference?

Half the second difference

If the second difference is 6, what is the coefficient of n2n^2?

3

For sequence 1, 6, 15, 28, 45, what are the second differences?

4, 4, 4

For sequence 3, 10, 21, 36, what is the value of aa in Tn=an2+bn+cT_n = an^2 + bn + c?

2

What is the nth term formula for sequence 3, 10, 21, 36?

Tn=2n2+nT_n = 2n^2 + n

For sequence 5, 8, 13, 20, 29, what are the first differences?

3, 5, 7, 9

What is the nth term formula for sequence 5, 8, 13, 20, 29?

Tn=n2+4T_n = n^2 + 4

What should you always check first to identify a quadratic sequence?

If second differences are constant

In what practical contexts do quadratic sequences often appear?

Tiling patterns

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