Worksheet: Finding the nth Term of an Arithmetic Sequence, Set 5

Topic

Sequences and Series

Description

Set 5 of this worksheet series delves even deeper into the concept of finding the nth term of an arithmetic sequence, presenting more challenging problems and real-world scenarios. This skill is fundamental in mathematics, serving as a cornerstone for understanding linear relationships and progressions in various contexts.

The formula a_n = a + (n - 1)d is a powerful tool for modeling and predicting linear growth or decay. In finance, it can be used to calculate annuities or analyze linear depreciation. In social sciences, it can represent steady demographic changes or linear trends in public opinion polls. Understanding arithmetic sequences is also crucial in computer programming, particularly in loop structures and certain algorithms.

Teacher's Script: "Let's explore a complex scenario. A company's profit is increasing by $5000 each quarter. In the 3rd quarter, they made $35,000, and in the 7th quarter, they made $55,000. To find the general term, we first confirm the common difference: (55,000 - 35,000) ÷ (7 - 3) = 5000. Using the 3rd term, we find the first term: 35,000 = a + (3 - 1)5000, so a = 25,000. Our nth term formula is a_n = 25,000 + (n - 1)5000 = 5000n + 20,000. This allows us to predict the company's profit for any given quarter!"

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.