Cubic Sequences (Leaving Cert Mathematics): Quizzes

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Cubic Sequences
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What defines a cubic sequence?

Third difference is constant

What type of sequence does the first difference of a cubic sequence form?

A quadratic sequence

What type of sequence does the second difference of a cubic sequence form?

A linear (arithmetic) sequence

What is the general term formula for a cubic sequence?

Tn=an3+bn2+cn+dT_n = an^3 + bn^2 + cn + d

What does the third difference equal in terms of coefficient aa?

6a6a

For sequence -1, 13, 51, 125, 247, ..., what is the third difference?

12

If the third difference is 12, what is the value of aa?

a=2a = 2

How many equations are needed to solve for bb, cc, and dd?

Three equations

Which terms should be substituted to form the required equations?

T1T_1, T2T_2, T3T_3

What is the general term for sequence -1, 13, 51, 125, 247, ...?

Tn=2n3−3T_n = 2n^3 - 3

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