Quadratic Sequences (Junior Cert Mathematics): Quizzes

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Quadratic Sequences
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What makes a sequence quadratic?

Second differences are constant

For the sequence 4,7,12,19,28,...4, 7, 12, 19, 28, ..., what are the second differences?

2,2,22, 2, 2

What is the general formula for a quadratic sequence?

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

In the formula Tn=an2+bn+cT_n = an^2 + bn + c, what does TnT_n represent?

The term you're trying to find

What does 2a2a equal in a quadratic sequence?

The second difference

For sequence 4,7,12,19,28,...4, 7, 12, 19, 28, ... with second difference 22, what is aa?

a=1a = 1

For Tn=n2+bn+cT_n = n^2 + bn + c, using T1=4T_1 = 4, what equation do you get?

b+c=3b + c = 3

In the worked example for 4,7,12,19,28,...4, 7, 12, 19, 28, ..., what is bb?

b=0b = 0

In the worked example for 4,7,12,19,28,...4, 7, 12, 19, 28, ..., what is cc?

c=3c = 3

What is the formula for the sequence 4,7,12,19,28,...4, 7, 12, 19, 28, ...?

Tn=n2+3T_n = n^2 + 3

Using Tn=n2+3T_n = n^2 + 3, what is T3T_3?

T3=12T_3 = 12

What should you always do after finding the formula for a quadratic sequence?

Double-check by substituting back

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