Question

Sum of a geometric series calculator.

A. Geometric sequence sum
B. Series summation calculator
C. Sum of geometric progression
D. Geometric sum formula

Answer 1

To calculate the sum of a geometric series, you can use the formula S = a * (1 - r^n) / (1 - r), where S is the sum of the series, a is the first term, r is the common ratio, and n is the number of terms.

Step-by-step explanation:

Sum of a Geometric Series

To calculate the sum of a geometric series, you can use the formula

S = a * (1 - r^n) / (1 - r)

, where

S

is the sum of the series,

a

is the first term,

r

is the common ratio, and

n

is the number of terms. Here are the steps to follow:

1. Identify the values of a, r, and n from the given geometric series.
2. Substitute the values into the formula S = a * (1 - r^n) / (1 - r).
3. Simplify the expression to find the sum of the geometric series S.

Example:

Let's say we have a geometric series with a first term

a = 2

, a common ratio

r = 3

, and

n = 4

terms. Using the formula, we can find the sum

S

:

S = 2 * (1 - 3^4) / (1 - 3)

S = 2 * (1 - 81) / -2

S = 2 * (-80) / -2

S = 80