How to determine the sum of a finite geometric sequence

The video tutorial explains how to determine the sum of a finite geometric series. It introduces two methods: manually adding terms and using a formula. The tutorial details the formula's application, including calculating the ratio and plugging values into the formula. It provides a step-by-step solution for a series with 12 terms, highlighting potential pitfalls and ensuring accuracy. The final sum is calculated, and the importance of using a calculator for large series is emphasized.

What mistake did the teacher make while calculating the final answer?

Explain the process of calculating the sum of the first 12 terms in the series.