1. What is a Geometric Sequence?

A geometric sequence is a sequence of numbers where each term after the first is found by multiplying the previous term by a fixed, non-zero number called the common ratio.

2. Recursive vs Explicit Formulas

Recursive Formula: Defines each term based on the previous term

Explicit Formula: Defines any term directly using its position

3. How the Calculator Works

The calculator takes the first term and common ratio, then generates both recursive and explicit formulas along with the first 5 terms of the sequence.

4. Using the Calculator

Tips: Enter the first term and common ratio. The common ratio cannot be zero. The calculator will display both recursive and explicit formulas along with the first 5 terms.

5. Frequently Asked Questions (FAQ)

Q1: What is the common ratio?
A: The common ratio (r) is the constant factor between consecutive terms in a geometric sequence.

Q2: Can the common ratio be negative?
A: Yes, a negative common ratio creates an alternating sequence where terms switch between positive and negative.

Q3: What if the common ratio is between 0 and 1?
A: The sequence will be decreasing (if first term is positive) and approach zero as n increases.

Q4: What if the common ratio is greater than 1?
A: The sequence will be increasing (if first term is positive) and grow without bound.

Q5: When would I use recursive vs explicit formulas?
A: Recursive formulas are useful for step-by-step calculations, while explicit formulas are better for finding specific terms directly.