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Gr 11 Math Ch 3: Quadratic Sequences

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Questions and Answers

What is the defining characteristic of a quadratic sequence?

The sequence is always increasing.

The second difference between any two consecutive terms is constant. (correct)

The first difference between any two consecutive terms is constant.

The sequence begins with a constant term.

What is the general form of the nth term of a quadratic sequence?

Tn = an^2 + bn + c (correct)

Tn = an^2 - bn + c

Tn = an + bn^2

Tn = an^3 + bn^2 + c

How can you determine the values of a, b, and c in a quadratic sequence?

By solving simultaneous equations derived from the first few terms (correct)

By graphing the sequence and finding the vertex

By using the formula Tn = an^2 + bn + c

By finding the average of the first few terms

What is the first difference in a quadratic sequence?

The difference between consecutive terms Signup and view all the answers

What can be said about the second differences in a quadratic sequence?

They are always constant. Signup and view all the answers

What is the purpose of finding the first difference in a quadratic sequence?

To find the second difference of the sequence. Signup and view all the answers

If a quadratic sequence has the terms 2, 5, 10, and 17, what can be said about the sequence?

The sequence is quadratic. Signup and view all the answers

What is the advantage of knowing the general term of a quadratic sequence?

It allows us to find any term in the sequence without knowing the preceding terms. Signup and view all the answers

How many terms of a quadratic sequence are needed to determine the values of a, b, and c?

3 Signup and view all the answers

What is the relationship between the general term of a quadratic sequence and the values of a, b, and c?

The general term is dependent on the values of a, b, and c. Signup and view all the answers

If a quadratic sequence has the terms 3, 6, 11, and 18, what is the value of the second term in the sequence when the first term is 5?

9 Signup and view all the answers

Which of the following is a condition for a sequence to be quadratic?

The second difference is constant. Signup and view all the answers

If the nth term of a quadratic sequence is given by $T_n = an^2 + bn + c$, what can be said about the coefficients a, b, and c?

They are dependent on the values of the first few terms. Signup and view all the answers

What is the purpose of finding the general term of a quadratic sequence?

To find any term in the sequence. Signup and view all the answers

If a quadratic sequence has the terms 1, 4, 9, and 16, what can be said about the sequence?