Worksheet: Finding the nth Term of an Arithmetic Sequence, Set 3

Topic

Sequences and Series

Description

Set 3 of this worksheet series delves deeper into the intricacies of finding the nth term of an arithmetic sequence. Students are presented with more complex scenarios, encouraging them to apply their understanding of the formula a_n = a + (n - 1)d in diverse contexts.

This skill is fundamental in mathematics, serving as a gateway to more advanced concepts in algebra and calculus. In real-world applications, arithmetic sequences can model uniform motion in physics, linear population growth in biology, or constant rate of change in various economic scenarios. Understanding how to derive and use the nth term formula enhances students' ability to analyze and predict trends in these fields.

Teacher's Script: "Let's tackle a real-world problem. A company starts with 100 employees and plans to hire 5 new employees each month. We can represent this as an arithmetic sequence where a = 100 and d = 5. Our nth term formula is a_n = 100 + (n - 1)5 = 5n + 95. Now, if we want to know how many employees they'll have after 1 year, we can simply plug in n = 12: a₁₂ = 5(12) + 95 = 155 employees."

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.