Question

Determine if the sequence below is arithmetic or geometric and determine the common difference/ratio in simplest form. 16, 8, 4, ...

a) Arithmetic; -2
b) Arithmetic; 2
c) Geometric; -2
d) Geometric; 2

Answer 1

The sequence is geometric with a ratio of 2.

Step-by-step explanation:

The given sequence is 16, 8, 4, ...

To determine if the sequence is arithmetic or geometric, we need to check if there is a common difference or ratio between the terms. In an arithmetic sequence, there is a constant difference between each term. In a geometric sequence, there is a constant ratio between each term.

In this sequence, 16 ÷ 8 = 8 ÷ 4 = 2. The terms are divided by 2 each time, which means the sequence is geometric with a ratio of 2.