Worksheet: Finding the nth Term of an Arithmetic Sequence, Set 16

Topic

Sequences and Series

Description

This worksheet continues the exploration of finding the nth term of arithmetic sequences, presenting advanced problems that challenge students to apply their knowledge in complex scenarios. The theory behind finding the nth term of a sequence is based on recognizing the linear relationship between the term number and its value. In an arithmetic sequence, this relationship is expressed as a_n = a + (n - 1)d, where a is the first term, n is the term number, and d is the common difference.

Understanding this concept is crucial in mathematics as it allows for the prediction of future terms in a sequence without having to calculate each intervening term. This skill has applications in various fields, including finance for calculating compound interest, physics for modeling uniform motion, and computer science for analyzing algorithm complexity.

Teacher's Script: "Let's consider a sequence where the 6th term is 31 and the 11th term is 51. To find the nth term, we first calculate the common difference: (51 - 31) ÷ (11 - 6) = 4. Using the 6th term, we can find the first term: 31 = a + (6 - 1)4, so a = 11. Our general formula is thus a_n = 11 + (n - 1)4 = 4n + 7. This allows us to find any term in the sequence without listing them all!"

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.