Question

A sequence is shown in the graph.

Assuming the pattern continues, what is the formula for the nth term?

A. an = 6(2n)
B. an = 2(6n − 1)
C. an = 6(0.5n − 1)
D. an = 6(0.5n + 1)

Answer 1

Answer: Choice C

Step-by-step explanation:

Focus on the y coordinates. They are: 6, 3, 1.5, 0.75

Divide each by their previous term

• 3/6 = 0.5
• 1.5/3 = 0.5
• 0.75/1.5 = 0.5

We have a common ratio of r = 0.5

This proves we have a geometric sequence.

The starting term is a = 6

The nth term is
`a_n = a(r)^(n-1) = 6(0.5)^(n-1)` which is likely what choice C is showing. Though choice C should be written as 6(0.5)^(n-1)