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Arithmetic and Geometric Sequences: Tutorial

Write a general form of an explicit function for the [tex]$n$[/tex]th term of any arithmetic sequence in terms of [tex]$a$[/tex] and [tex]$d$[/tex]. Use the form below to write your function. Type the correct answer in the box.

[tex]\[
f(n) =
\][/tex]

Sagot :

GinnyAnsweridn
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].
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