Certainly! In an arithmetic sequence, each term after the first is obtained by adding a constant difference, [tex]\( d \)[/tex], to the previous term.
The general form of an arithmetic sequence can be given by:
[tex]\[ a_n = a + (n - 1)d \][/tex]
where:
- [tex]\( a_n \)[/tex] is the [tex]\( n \)[/tex]th term of the sequence,
- [tex]\( a \)[/tex] is the first term of the sequence,
- [tex]\( d \)[/tex] is the common difference between consecutive terms,
- [tex]\( n \)[/tex] is the position of the term in the sequence.
So, the function for the [tex]\( n \)[/tex]th term of any arithmetic sequence in terms of [tex]\( a \)[/tex] and [tex]\( d \)[/tex] is:
[tex]\[ f(n) = a + (n - 1)d \][/tex]
This formula allows you to calculate the [tex]\( n \)[/tex]th term by substituting the values of [tex]\( a \)[/tex], [tex]\( d \)[/tex], and [tex]\( n \)[/tex].
