Worksheet: Finding the nth Term of an Arithmetic Sequence, Set 19

Topic

Sequences and Series

Description

Set 19 of this worksheet series presents students with highly challenging problems related to finding the nth term of arithmetic sequences. The theory behind this concept is based on the principle of constant difference between consecutive terms. The formula a_n = a + (n - 1)d encapsulates this concept, where a is the initial term, n is the term number, and d is the common difference. This algebraic representation allows us to model linear growth or decay in a concise, powerful way.

This understanding is vital in various fields. In physics, it can model uniform motion or constant acceleration. In social sciences, it can represent steady demographic changes or linear trends in public opinion polls. In computer programming, it's crucial for loop structures and certain algorithms.

Teacher's Script: "Consider a complex scenario where we know the sum of the 3rd and 7th terms is 50, and the 12th term is 62. To find the nth term, we first set up equations: (a + 2d) + (a + 6d) = 50 and a + 11d = 62. Solving these simultaneously, we find a = 7 and d = 5. Our general formula is thus a_n = 7 + (n - 1)5 = 5n + 2. This example shows how we can derive the formula even with limited and indirect information about the sequence!"

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.