What is the summation formula for a geometric series?

What is the summation formula for a geometric series?

• A. Sn = (a1 - r^n) / (1 - r)
• B. Sn = a1 * (1 - r^n) / (1 - r)
• C. Sn = n * a1
• D. Sn = (a1 + r^n) / (1 + r)

Answer: (B)

The summation formula for a geometric series is indeed represented by the option that states Sn = a1 * (1 - r^n) / (1 - r). This formula provides a way to calculate the sum of the first n terms of a geometric series, where "a1" is the first term, "r" is the common ratio between the terms, and "n" is the number of terms. To understand this formula, let's break it down. In a geometric series, each term after the first is found by multiplying the previous term by a constant ratio (r). The series starts with the first term "a1," and the subsequent terms will follow the pattern: a1, a1 * r, a1 * r^2, ..., up to a1 * r^(n-1). The factor (1 - r^n) in the numerator reflects the contribution of the terms from the series, where r^n indicates how the terms grow and are scaled down when multiplied by the first term (a1). The denominator (1 - r) normalizes this growth by accounting for the common ratio; it shows how the series converges when r is less than 1 or diverges otherwise. This

The summation formula for a geometric series is indeed represented by the option that states Sn = a1 * (1 - r^n) / (1 - r). This formula provides a way to calculate the sum of the first n terms of a geometric series, where "a1" is the first term, "r" is the common ratio between the terms, and "n" is the number of terms.

To understand this formula, let's break it down. In a geometric series, each term after the first is found by multiplying the previous term by a constant ratio (r). The series starts with the first term "a1," and the subsequent terms will follow the pattern: a1, a1 * r, a1 * r^2, ..., up to a1 * r^(n-1).

The factor (1 - r^n) in the numerator reflects the contribution of the terms from the series, where r^n indicates how the terms grow and are scaled down when multiplied by the first term (a1). The denominator (1 - r) normalizes this growth by accounting for the common ratio; it shows how the series converges when r is less than 1 or diverges otherwise.

This