1. What is the Nth Term of a Fraction Sequence?

The nth term of a fraction sequence is a formula that allows you to calculate any term in the sequence directly, without having to work out all the previous terms. For linear fraction sequences, the nth term follows the form (a/b)n + (c/d).

2. How Does the Calculator Work?

The calculator uses the linear fraction sequence formula:

Where:

• \( \frac{a}{b} \) — The coefficient of n (fraction)
• \( \frac{c}{d} \) — The constant term (fraction)
• \( n \) — The term number you want to find

Explanation: The calculator combines the fractions, simplifies the result, and presents it in its simplest form.

3. Importance of Finding the Nth Term

Details: Finding the nth term is essential for predicting future terms in a sequence, analyzing patterns, and solving problems in algebra and number theory.

4. Using the Calculator

Tips: Enter the coefficients as fractions (a/b and c/d) and the term number n. The calculator will return the nth term in its simplest fractional form.

5. Frequently Asked Questions (FAQ)

Q1: What if my sequence isn't linear?
A: This calculator works for linear sequences. For quadratic or other patterns, you'll need a different approach.

Q2: How do I find the coefficients from a sequence?
A: For linear sequences, the coefficient is the difference between terms, and the constant is found by substituting back.

Q3: Can this handle improper fractions?
A: Yes, the calculator works with proper and improper fractions, always simplifying the result.

Q4: What if denominators are negative?
A: Negative denominators are automatically converted to positive by adjusting the numerator.

Q5: Can I use decimals instead of fractions?
A: This calculator is designed specifically for fraction inputs. For decimal sequences, use a different calculator.