Worksheet: Finding the nth Term of an Arithmetic Sequence, Set 15

Topic

Sequences and Series

Description

The final set in this comprehensive series on finding the nth term of arithmetic sequences presents the most challenging and complex problems. The theory behind finding the nth term is grounded in the principle of linear progression. The formula a_n = a + (n - 1)d represents this linear relationship, allowing us to predict any term in the sequence based on its position and the sequence's characteristics.

This concept is fundamental in mathematics and has wide-ranging applications. In finance, it can be used to calculate annuities or analyze linear depreciation. In urban planning, it can model the growth of traffic congestion over time. In data science, it forms the basis for understanding more complex sequences and series used in predictive modeling.

Teacher's Script: "Let's explore a challenging scenario. A company's profit is increasing by $3000 each quarter. In the 2nd quarter, they made $28,000, and in the 8th quarter, they made $58,000. To find the general term, we first confirm the common difference: (58,000 - 28,000) ÷ (8 - 2) = 5000. Using the 2nd term, we find the first term: 28,000 = a + (2 - 1)5000, so a = 23,000. Our nth term formula is a_n = 23,000 + (n - 1)5000 = 5000n + 18,000. This allows us to predict the company's profit for any given quarter, demonstrating the power of arithmetic sequences in financial modeling!"

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.