Using n-th Terms of Linear Sequences

Using n-th Terms of Linear Sequences

Basic Concepts

  • A Linear Sequence is a sequence where the difference between two consecutive terms is constant.
  • The term-to-term rule can be used to find subsequent terms.
  • The n-th term of a sequence is a formula that gives the position of a term in a sequence.

Identifying the nth Term

  • To identify the nth term of a linear sequence, one must find the common difference.
  • The Common Difference is found by subtracting each preceding term from the following term.

Forming nth Term

  • To form the nth term of a sequence, identify the common difference and the first term.
  • The nth term of a linear sequence can be written in the form an + b, where a is the common difference and b is a constant.
  • a is often the multiplier in the term-to-term rules, while b is the starting number of the sequence.

Using nth Term

  • The nth term can be used to find any term in a sequence without having to know the previous terms.
  • Simply replace n with the position of the term you are trying to find.
  • For instance to find the 10th term, replace n with 10 in the formula an + b.

Testing nth term

  • If you have found the nth term, you can verify it by trying it on one or more terms in the sequence.
  • If the formula gives the correct output, then the nth term is very likely correctly identified.

Understanding Problem Solving with nth Term

  • Often various problems will make use of the nth term, such as finding the sum of the first n terms.
  • Read these problems carefully to identify and understand what is required.

Students must understand that identifying the n-th term of a sequence is crucial as it enables you to generate any term in that sequence and helps with understanding the characteristics of the sequence.