1. What Is a Fraction Sequence?

A fraction sequence is an ordered list of fractions where each term after the first is found by adding a constant fractional difference to the preceding term. This calculator helps you find any term in such a sequence.

2. How Does the Calculator Work?

The calculator uses the arithmetic sequence formula adapted for fractions:

Where:

• \( \frac{a}{b} \) — First term of the sequence
• \( \frac{c}{d} \) — Common difference between terms
• \( n \) — Term number to find

Explanation: The formula calculates the nth term by starting with the first term and adding the common difference multiplied by (n-1) times.

3. Importance of Finding the Nth Term

Details: Being able to find any term in a sequence is fundamental in mathematics, with applications in algebra, calculus, and real-world problems involving patterns and progressions.

4. Using the Calculator

Tips: Enter the numerator and denominator for both the first term and the common difference. Then enter which term number you want to find. All denominators must be positive integers.

5. Frequently Asked Questions (FAQ)

Q1: Can this calculator handle negative fractions?
A: Yes, the calculator works with both positive and negative fractions.

Q2: What if my sequence isn't arithmetic?
A: This calculator only works for arithmetic sequences (constant difference between terms). For geometric sequences (constant ratio), a different calculator would be needed.

Q3: How does the calculator simplify fractions?
A: The calculator reduces fractions to their simplest form by dividing numerator and denominator by their greatest common divisor (GCD).

Q4: What if I get a whole number result?
A: If the denominator simplifies to 1, the calculator displays the result as a whole number for clarity.

Q5: Can I find terms beyond the 100th term?
A: Yes, the calculator can compute terms for any positive integer n, though very large numbers may be limited by your browser's capabilities.