Using n-th Terms of Linear Sequences
- 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
ais the common difference and
bis a constant.
ais often the multiplier in the term-to-term rules, while
bis 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
nwith the position of the term you are trying to find.
- For instance to find the 10th term, replace
nwith 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.