1. What is a Quadratic Sequence?

A quadratic sequence is a sequence of numbers where the second difference between terms is constant. The nth term of a quadratic sequence is given by the formula aₙ = an² + bn + c, where a, b, and c are constants.

2. How Does the Calculator Work?

The calculator uses the quadratic sequence formula:

Where:

• \( a \) — Coefficient of n²
• \( b \) — Coefficient of n
• \( c \) — Constant term
• \( n \) — Term number in the sequence

Explanation: The formula calculates the value of any term in a quadratic sequence given its position (n) and the coefficients.

3. Importance of Quadratic Sequences

Details: Quadratic sequences appear in various mathematical and real-world applications, including physics (projectile motion), computer science (algorithm complexity), and finance (compound interest models).

4. Using the Calculator

Tips: Enter the coefficients a, b, and c, along with the term number n you want to calculate. The term number must be a positive integer.

5. Frequently Asked Questions (FAQ)

Q1: How do I find the coefficients from a sequence?
A: For a sequence, calculate the second differences. The coefficient a is half the second difference. Then use known terms to solve for b and c.

Q2: What's the difference between linear and quadratic sequences?
A: Linear sequences have constant first differences (arithmetic sequences), while quadratic sequences have constant second differences.

Q3: Can this calculator find terms for non-integer n?
A: Yes, the calculator works for any real number n, though sequences typically use positive integers.

Q4: How accurate are the results?
A: Results are accurate to 4 decimal places. For exact fractions, manual calculation may be needed.

Q5: Can this be used for cubic sequences?
A: No, this calculator is specifically for quadratic sequences. Cubic sequences require an n³ term.