1. What is a Quadratic Sequence?

A quadratic sequence is a sequence where the second difference between terms is constant. The general form is Tₙ = an² + bn + c, where a, b, and c are constants, and n is the term number.

2. How Does the Calculator Work?

The calculator solves for a, b, and c in the quadratic formula using the first three terms of the sequence:

Where:

• \( T_1 \) — First term of the sequence
• \( T_2 \) — Second term of the sequence
• \( T_3 \) — Third term of the sequence
• \( a \) — Quadratic coefficient (n² term)
• \( b \) — Linear coefficient (n term)
• \( c \) — Constant term

Explanation: The calculator solves this system of equations to find the values of a, b, and c that define the quadratic sequence.

3. Importance of Finding the Nth Term

Details: Finding the nth term formula allows you to calculate any term in the sequence without listing all previous terms, which is essential for analyzing patterns and making predictions.

4. Using the Calculator

Tips: Enter the first three terms of your quadratic sequence. The calculator will determine the coefficients and display the complete nth term formula.

5. Frequently Asked Questions (FAQ)

Q1: How do I know if a sequence is quadratic?
A: Calculate the second differences between terms. If they're constant, the sequence is quadratic.

Q2: What if I have more than three terms?
A: The first three terms are sufficient to determine a quadratic sequence. Additional terms can be used to verify the formula.

Q3: Can this calculator handle non-quadratic sequences?
A: No, it's designed specifically for quadratic sequences. For arithmetic sequences (linear), use a different calculator.

Q4: What if the sequence isn't perfectly quadratic?
A: The calculator will still provide coefficients, but they may not accurately predict subsequent terms if the sequence isn't truly quadratic.

Q5: Can I find specific terms with this formula?
A: Yes, once you have the formula Tₙ = an² + bn + c, you can substitute any positive integer n to find that term.