# MA.912.AR.10.2

Given a mathematical or real-world context, write and solve problems involving geometric sequences.

### Examples

A bacteria in a Petri dish initially covers 2 square centimeters. The bacteria grows at a rate of 2.6% every day. Determine the geometric sequence that describes the area covered by the bacteria after 0,1,2,3… days. Determine using technology, how many days it would take the bacteria to cover 10 square centimeters.
General Information
Subject Area: Mathematics (B.E.S.T.)
Strand: Algebraic Reasoning
Date Adopted or Revised: 08/20
Status: State Board Approved

## Benchmark Instructional Guide

### Terms from the K-12 Glossary

•  Geometric sequence

### Vertical Alignment

Previous Benchmarks

Next Benchmarks

### Purpose and Instructional Strategies

In Algebra I, students worked with exponential relationships. In Math for Data and Financial Literacy, students write and solve problems using geometric sequences.
• Instruction focuses on real-world contexts involving geometric sequences (MTR.7.1).
• Students may use a variety of representations to solve problems such as writing out the sequence or using the explicit formula. The focus of the benchmark is to understand geometric sequences and how they connect to exponential equations (MTR.2.1)
• In cases where the student is solving for time, students can use logarithms, or can use technology, such as an online or handheld graphing calculator, to solve with a graph, table or substitution.

### Common Misconceptions or Errors

• Students may mistake a geometric model for an arithmetic model.
• Students may forget to convert the percent to a decimal when performing calculations.
• Students may forget to add 1 to the rate when a geometric sequence is growing or to subtract the rate from 1 when the sequence models a decay model.
• Students may have trouble using technology to determine a value when solving for time.

Instructional Task 1 (MTR.2.1, MTR.5.1, MTR.7.1
• In January, Juan put \$1200 in a savings account that pays 3.0% interest once at the end of each year. Assuming Juan has no other deposits or withdrawals, answer the following.
• Part A. Determine the geometric sequence that describes the amount of money in his account after 0, 1, 2, 3… years.
• Part B. How long will it take for Juan to double his money?

### Instructional Items

Instructional Item 1
• A company starts a new website. On the first day of the website being published, the site has 250 visitors. The company estimates that the number of visits to the website will increase 5% each day.
• Part A. Write a sequence that describes the number of visits on each of the first 5 days.
• Part B. How long will it take for the website to have 1,000 visits in a single day?

*The strategies, tasks and items included in the B1G-M are examples and should not be considered comprehensive.

## Related Courses

This benchmark is part of these courses.
1200340: Algebra 2 Honors (Specifically in versions: 2014 - 2015, 2015 - 2022, 2022 and beyond (current))
1200400: Foundational Skills in Mathematics 9-12 (Specifically in versions: 2014 - 2015, 2015 - 2022, 2022 and beyond (current))
1202340: Precalculus Honors (Specifically in versions: 2014 - 2015, 2015 - 2022, 2022 and beyond (current))
1212300: Discrete Mathematics Honors (Specifically in versions: 2022 and beyond (current))
1200388: Mathematics for Data and Financial Literacy Honors (Specifically in versions: 2022 and beyond (current))
1200384: Mathematics for Data and Financial Literacy (Specifically in versions: 2022 and beyond (current))
1209315: Mathematics for ACT and SAT (Specifically in versions: 2022 and beyond (current))

## Related Access Points

Alternate version of this benchmark for students with significant cognitive disabilities.

## Related Resources

Vetted resources educators can use to teach the concepts and skills in this benchmark.

## Tutorial

Geometric sequence or progression:

We will learn how to write a geometric sequence.

Type: Tutorial

## Student Resources

Vetted resources students can use to learn the concepts and skills in this benchmark.

## Tutorial

Geometric sequence or progression:

We will learn how to write a geometric sequence.

Type: Tutorial

## Parent Resources

Vetted resources caregivers can use to help students learn the concepts and skills in this benchmark.