Answer:
We are used to describing arithmetic sequences like this:
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 nnn to represent any term number and a(n)a(n)a, left parenthesis, n, right parenthesis to represent the n^\text{th}n
th
n, 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, ...
nnn a(n)a(n)a, left parenthesis, n, right parenthesis
(The term number) (The n^\text{th}n
th
n, start superscript, start text, t, h, end text, end superscript term)
111 333
222 555
333 777
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, left parenthesis, n, right parenthesis for any possible nnn.
Check your understanding
1) Find a(4)a(4)a, left parenthesis, 4, right parenthesis in the sequence 3, 5, 7, ...
a(4)=a(4)=a, left parenthesis, 4, right parenthesis, equals
[I need help!]
2) For any term number nnn, what does a(n-1)a(n−1)a, left parenthesis, n, minus, 1, right parenthesis represent?
