Respuesta :
Answer:
The recursive formula of the arithmetic sequence is
[tex]\left\{ \begin{array}{ll} c(1)=-16 & \\ c(n)=c(n-1)-17 \end{array} \right.[/tex]
Step-by-step explanation:
A recursive formula designates the starting term, [tex]a_1[/tex], and the nth term of the sequence, [tex]a_n[/tex], as an expression containing the previous term (the term before it), [tex]a_{n-1}[/tex].
Recursive formulas give us two pieces of information:
- The first term of the sequence
- The pattern rule to get any term from the term that comes before it
From the arithmetic sequence [tex]-16,-33,-50,-67,...[/tex], the first term is -16 and the rule to get any term from its previous term is add -17.
Therefore, the recursive formula should look as follows:
[tex]\left\{ \begin{array}{ll} c(1)=-16 & \\ c(n)=c(n-1)-17 \end{array} \right.[/tex]
