Answer:
In an arithmetic sequence, the difference between consecutive terms is constant. In the sequence you provided (3, 6, 9, 12, 15), each number increases by 3, which is called the common difference.
To find the nth term of an arithmetic sequence, we use the formula:
[tex]a_{n}[/tex] = [tex]a_{1}[/tex] [tex](n - 1)_{d}[/tex]
where:
[tex]a_{n}[/tex] is the nth term,
[tex]a_{1}[/tex] is the first term,
n is the term number,
d is the common difference.
For your sequence:
The first term [tex]a_{1}[/tex] is 3.
The common difference is 3.
So the formula becomes:
[tex]a_{n}[/tex] = 3 + ( − 1) ⋅ 3
Simplifying the formula gives:
[tex]a_{n}[/tex] = [tex]3_{n}[/tex]
This formula tells us that to get the nth term, we simply multiply 3 by the term number .
