Worksheet: Finding the nth Term of an Arithmetic Sequence, Set 9

Topic

Sequences and Series

Description

Set 9 continues to challenge students with high-level problems involving arithmetic sequences. These exercises require students to apply their knowledge of the nth term formula in innovative ways, often combining it with other mathematical concepts.

The ability to work with arithmetic sequences and apply the formula a_n = a + (n - 1)d is crucial in many areas of mathematics and its applications. It forms the foundation for understanding more complex sequences and series, as well as linear functions and progressions.

Teacher's Script: "Imagine a city's population is decreasing by 1,500 people each year. If the population in 2025 is projected to be 250,000, and in 2030 it's expected to be 242,500, can we find a general formula for the population? Let's use our arithmetic sequence knowledge. We have a₁ + 4d = 250,000 and a₁ + 9d = 242,500. Solving these, we get a₁ = 256,000 and d = -1,500. Our formula is thus P(n) = 256,000 + (n - 1)(-1,500) = 257,500 - 1,500n, where n is the number of years since 2024."

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.