# Lesson 26

Using the Sum

This lesson builds on what students learned about calculating the sum of the first $$n$$ terms of a geometric sequence in the previous lesson. Students apply the formula for the sum, $$s = a \frac{1-r^{n}}{1-r}$$ , to both mathematical and real world situations, building fluency in its use and a greater understanding of the nature of geometric sequences, focusing on those with a common ratio greater than 1. In the last activity, students begin by making a prediction about the amount of yearly investment needed to reach $100,000 by the time they are 70. Putting boundaries on possible outcomes of a problem is an important aspect of mathematical modeling (MP4). Students return to their prediction at the conclusion of the lesson as they make sense of the nature of geometric sequences and how they change (MP1). This context connects students back to the work they did with investments earlier in the unit. Now students have new tools for analyzing more complex investment scenarios. Technology isn't required for this lesson, but there are opportunities for students to choose to use appropriate technology to solve problems. We recommend making technology available. ### Learning Goals Teacher Facing • Calculate solutions to problems by using the formula for the first$n\$ terms in a geometric sequence.
• Interpret results about geometric sums in non-mathematical contexts.

### Student Facing

• Let’s calculate some totals.

### Student Facing

• I can use the geometric sum formula to solve problems.