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 constant called the common ratio. The sum of the first n terms of a geometric sequence can be calculated using the formula provided.

2. How Does the Calculator Work?

The calculator uses the geometric sequence sum formula:

Where:

• \( a \) — The first term of the sequence
• \( r \) — The common ratio between terms
• \( n \) — The number of terms to sum

Explanation: The formula calculates the sum by accounting for the multiplicative nature of the sequence and the number of terms included in the sum.

3. Importance of Geometric Sequences

Details: Geometric sequences are fundamental in mathematics and appear in many real-world applications including finance (compound interest), computer science (algorithm analysis), physics (exponential decay), and biology (population growth).

4. Using the Calculator

Tips: Enter the first term (a), common ratio (r), and number of terms (n). The common ratio cannot be 1 (for r=1, the sum is simply a×n).

5. Frequently Asked Questions (FAQ)

Q1: What if the common ratio is 1?
A: When r=1, the sequence becomes a constant sequence and the sum is simply a×n.

Q2: Can this calculator handle infinite series?
A: No, this calculates finite sums. For infinite series (|r| < 1), the sum is a/(1-r).

Q3: What about negative common ratios?
A: The formula works for both positive and negative ratios (except r=1).

Q4: How precise are the calculations?
A: Results are rounded to 4 decimal places for clarity.

Q5: Can I use this for financial calculations?
A: Yes, this can model compound interest scenarios where payments remain constant.