Worksheet: Finding the nth Term of an Arithmetic Sequence, Set 2

Topic

Sequences and Series

Description

This worksheet builds upon the concepts introduced in Set 1, providing more challenging exercises for identifying and analyzing arithmetic sequences. Students continue to work with the formula a_n = a + (n - 1)d, developing a deeper understanding of how to apply it in various contexts.

The ability to find the nth term of an arithmetic sequence is a powerful tool in mathematics. It allows students to make predictions and solve problems involving linear patterns. This skill is particularly useful in fields such as economics, where it can be applied to analyze trends in market data or calculate fixed-rate mortgages.

Teacher's Script: "Imagine we have a sequence where the 3rd term is 15 and the 7th term is 31. Can we find the nth term? First, let's calculate the common difference: (31 - 15) ÷ (7 - 3) = 4. Now, we can use the 3rd term to find the first term: 15 = a + (3 - 1)4, so a = 7. Our nth term formula is therefore a_n = 7 + (n - 1)4 = 4n + 3."

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.