Question

Complete the recursive formula of the arithmetic sequence, -16,-33,-50,-67,...

Answer 1

Answer:

The recursive formula of the arithmetic sequence is

$\left\{ \begin{array}{ll} c(1)=-16 & \\ c(n)=c(n-1)-17 \end{array} \right.$

Step-by-step explanation:

A recursive formula designates the starting term, $a_1$, and the nth term of the sequence, $a_n$, as an expression containing the previous term (the term before it), $a_{n-1}$.

Recursive formulas give us two pieces of information:

1. The first term of the sequence
2. The pattern rule to get any term from the term that comes before it

From the arithmetic sequence $-16,-33,-50,-67,...$, 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:

$\left\{ \begin{array}{ll} c(1)=-16 & \\ c(n)=c(n-1)-17 \end{array} \right.$