Worksheet: Finding the nth Term of an Arithmetic Sequence, Set 17

Topic

Sequences and Series

Description

Set 17 of this worksheet series delves deeper into the intricacies of arithmetic sequences. The theory behind finding the nth term involves recognizing that each term in an arithmetic sequence is a linear function of its position. This concept is encapsulated in the formula a_n = a + (n - 1)d, which represents the fundamental relationship between any term, its position, and the sequence's characteristics.

This understanding is essential in mathematics and its applications, as it allows for efficient analysis of linear growth patterns. In fields such as economics, it can be used to model steady growth or decline, while in physics, it can describe uniform motion or constant acceleration.

Teacher's Script: "Imagine we're analyzing a city's population decrease where they start with 500,000 residents and lose 2,000 people every year. We can model this with an arithmetic sequence where a = 500,000 and d = -2,000. Our nth term formula is a_n = 500,000 + (n - 1)(-2,000) = 502,000 - 2,000n. If we want to predict their population after 25 years, we calculate a₂₅ = 502,000 - 2,000(25) = 452,000 residents. This demonstrates how powerful our formula can be in making long-term predictions!"

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.