Episode 12 — Patterns and Sequences

Geometric Series

Learners will be able to:

• Calculate the sum of n terms of a geometric series using the formula Sn = a × (1 - r^n) / (1 - r), where r is not equal to one and lies between minus one and one. • Determine whether a given sequence is a geometric series by calculating the ratio of consecutive terms. • Use the correct formula for calculating the sum of n terms of a geometric series, either Sn = a × (r^n - 1) / (r - 1) when r is greater than one or Sn = a × (1 - r^n) / (1 - r) when r is less than one. • Apply the concept of a geometric series to solve real-world problems involving rewards or payments that increase by a constant ratio. • Evaluate the sum of n terms of a geometric series using a calculator, given the values of a and r.