Worksheet: Finding the nth Term of an Arithmetic Sequence, Set 13

Topic

Sequences and Series

Description

This worksheet continues to build on the concepts of arithmetic sequences, offering advanced problems that require students to apply their knowledge of the nth term formula in diverse and complex situations. The theory behind finding the nth term of a sequence is rooted in the concept of linear growth or decay. The formula a_n = a + (n - 1)d expresses this linear relationship, allowing us to generate any term in the sequence without having to list all preceding terms.

Understanding this concept is crucial in many fields. In environmental science, it can model the accumulation of pollutants over time. In finance, it's used to calculate fixed-rate loans or analyze linear trends in market data. In computer science, it plays a role in certain sorting algorithms and in analyzing time complexity.

Teacher's Script: "Let's tackle a real-world problem. A city's population is decreasing by 500 people each year. If the population in 2020 was 100,000, we can model this with an arithmetic sequence where a = 100,000 and d = -500. Our nth term formula is a_n = 100,000 + (n - 1)(-500) = 100,500 - 500n. If we want to predict when the population will drop below 90,000, we set up the inequality: 100,500 - 500n < 90,000. Solving this, we find n > 21. This means the population will drop below 90,000 in the 22nd year, or 2041."

For a complete collection of terms related to Sequences and Series click on this link: Finding the nth Term of an Arithmetic Sequence Worksheet Collection.