Worksheet: Finding the nth Term of an Arithmetic Sequence, Set 10

Topic

Sequences and Series

Description

The final set in this series, Set 10, presents the most challenging problems related to finding the nth term of arithmetic sequences. These exercises are designed to test and reinforce all the skills and concepts learned throughout the previous sets.

Mastery of arithmetic sequences and the formula a_n = a + (n - 1)d is essential for advanced mathematics and many real-world applications. It provides a strong foundation for understanding linear relationships, progressions, and more complex sequence types.

Teacher's Script: "For our final challenge, let's consider a sequence where the sum of the first three terms is 18, and the sum of the next three terms is 36. Can we find the nth term? We can set up the equations: (a + a + d + a + 2d) = 18 and (a + 3d + a + 4d + a + 5d) = 36. Solving these, we find a = 4 and d = 3. Therefore, our nth term formula is a_n = 4 + (n - 1)3 = 3n + 1. This problem demonstrates how we can derive the sequence formula even when given information about sums of terms rather than individual terms."

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.