Question

What is the recursive rule for the sequence shown in the graph?

Answer 1

`\textsf{C)} \quad a_n=a_(n-1)-4`

Explanation:

The plotted (n, a(n)) points on the given graph are:

• (1, 13)
• (2, 9)
• (3, 5)
• (4, 1)
• (5, -3)

From observation of these points, we can see that each successive term is obtained by subtracting 4 from the previous term. As there is a constant difference between terms, the sequence is arithmetic.

A recursive rule for an arithmetic sequence is a formula that generates each term in the sequence based on the previous term and a common difference.

The general formula for a recursive arithmetic sequence is:

`\large\boxed{a_n=a_(n-1)+d}`

where:

• 
  `a_n` is the nth term in the sequence.
• 
  `a_(n-1)` is the previous term (the term before ).
• d is the common difference.

Since the common difference between terms is -4, the recursive rule for the sequence shown in the graph is:

`\Large\boxed{\boxed{a_n=a_(n-1)-4}}`