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Questions and Answers
What is the defining characteristic of a quadratic sequence?
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?
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?
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?
What is the first difference in a quadratic sequence?
What can be said about the second differences in a quadratic sequence?
What can be said about the second differences in a quadratic sequence?
What is the purpose of finding the first difference in a quadratic sequence?
What is the purpose of finding the first difference in a quadratic sequence?
If a quadratic sequence has the terms 2, 5, 10, and 17, what can be said about the sequence?
If a quadratic sequence has the terms 2, 5, 10, and 17, what can be said about the sequence?
What is the advantage of knowing the general term of a quadratic sequence?
What is the advantage of knowing the general term of a quadratic sequence?
How many terms of a quadratic sequence are needed to determine the values of a, b, and c?
How many terms of a quadratic sequence are needed to determine the values of a, b, and c?
What is the relationship between the general term of a quadratic sequence and the values of a, b, and c?
What is the relationship between the general term of a quadratic sequence and the values of a, b, and c?
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?
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?
Which of the following is a condition for a sequence to be quadratic?
Which of the following is a condition for a sequence to be quadratic?
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?
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?
What is the purpose of finding the general term of a quadratic sequence?
What is the purpose of finding the general term of a quadratic sequence?
If a quadratic sequence has the terms 1, 4, 9, and 16, what can be said about the sequence?
If a quadratic sequence has the terms 1, 4, 9, and 16, what can be said about the sequence?
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