Question

larry is reviewing his cell phone bill. when he gets to the text message part, he notices that he sent 7 text messages in january, 35 text messages in february, 175 text messages in march, and 875 text messages in april. what kind of sequence is this? arithmetic geometric both neither

Explanation:

Step1: Recall arithmetic sequence definition

An arithmetic sequence has a common - difference \(d=a_{n + 1}-a_{n}\). Let \(a_1 = 7\), \(a_2=35\), \(a_3 = 175\), \(a_4=875\). Calculate differences: \(a_2 - a_1=35 - 7=28\), \(a_3 - a_2=175 - 35 = 140\). Since \(28
eq140\), there is no common - difference.

Step2: Recall geometric sequence definition

A geometric sequence has a common ratio \(r=\frac{a_{n + 1}}{a_{n}}\). Calculate ratios: \(\frac{a_2}{a_1}=\frac{35}{7}=5\), \(\frac{a_3}{a_2}=\frac{175}{35}=5\), \(\frac{a_4}{a_3}=\frac{875}{175}=5\). There is a common ratio of \(r = 5\).

Answer:

geometric