Question

determine if the sequence below is arithmetic or geometric and determine the common difference / ratio in simplest form. 4, 8, 12, ... answer attempt 1 out of 3 this is sequence and the is equal to . a geometric an arithmetic submit

Explanation:

Step1: Check for arithmetic sequence

To check if a sequence is arithmetic, we find the difference between consecutive terms. For the sequence \(4, 8, 12, \dots\), calculate \(8 - 4 = 4\) and \(12 - 8 = 4\). The difference between consecutive terms is constant (4).

Step2: Check for geometric sequence

To check if a sequence is geometric, we find the ratio between consecutive terms. Calculate \(\frac{8}{4} = 2\) and \(\frac{12}{8} = \frac{3}{2}\). The ratios are not constant, so it is not a geometric sequence.
Since the difference between consecutive terms is constant (4), the sequence is arithmetic with a common difference of 4.

Answer:

This is an arithmetic sequence and the common difference is equal to 4.