What is the pattern for this equation: f(n) = 2+3(n-1)

We are used to describing arithmetic sequences like this:

3,5,7,...3, 5, 7,...3,5,7,...3, comma, 5, comma, 7, comma, point, point, point

But there are other ways. In this lesson, we'll be learning two new ways to represent arithmetic sequences: recursive formulas and explicit formulas. Formulas give us instructions on how to find any term of a sequence.

To remain general, formulas use to represent any term number and a(n)a(n)a(n)a, left parenthesis, n, right parenthesis to represent the nthn^\text{th}nthn, start superscript, start text, t, h, end text, end superscript term of the sequence. For example, here are the first few terms of the arithmetic sequence 3, 5, 7, ...

a(n)a(n)a(n)a, left parenthesis, n, right parenthesis

(The term number)(The nthn^\text{th}nthn, start superscript, start text, t, h, end text, end superscript term)

11113333

22225555

33337777

We mentioned above that formulas give us instructions on how to find any term of a sequence. Now we can rephrase this as follows: formulas tell us how to find a(n)a(n)a(n)a, left parenthesis, n, right parenthesis for any possible .

Step-by-step explanation:

a negative exponent is translated as follows:

so, we have