Worksheet: Finding the nth Term of an Arithmetic Sequence, Set 4

Topic

Sequences and Series

Description

Set 4 of this worksheet series continues to explore the concept of finding the nth term of an arithmetic sequence, introducing more sophisticated problems and applications. This skill is crucial in mathematics, forming the basis for understanding linear relationships and progressions.

The ability to derive and use the formula a_n = a + (n - 1)d is essential in various fields. In urban planning, it can model the growth of traffic congestion over time. In environmental science, it can represent the steady accumulation or depletion of resources. In computer science, arithmetic sequences play a role in certain sorting algorithms and in analyzing time complexity.

Teacher's Script: "Consider a city's population that's 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 can 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.