A pattern can be represented with numbers, graphs, or objects and we can call it a sequence.
A sequence can often be defined using an equation or rule, where the term number is the input and the output is the term or term value. Typically, the term number for the first term is 1, but it does not have to be.
The explicit rule for a sequence tells us how to calculate the term value given the term number. We can write the explicit rule using subscript notation.
The sequence: -1, 4, 9, 14, ... has the explicit rule a_n=-6+5n where a_n represents the nth term, which gives:
Consider the sequence:
1, 4,9, 16, 25\ldots
Identify a_1 and a_4.
Find the next two terms in the sequence.
Write an explicit rule for the nth term of the sequence.
Find the first four terms of the sequence described by:
a_n = \dfrac{3 n - 1}{n^{2} + 4}