Question

is the sequence arithmetic: 78, 785, 7855, 78555, ... ?

Explanation:

Step1: Recall arithmetic sequence definition

An arithmetic sequence has a common difference \(d\), where \(d = a_{n + 1}-a_{n}\) for all \(n\), and \(d\) is constant.

Step2: Calculate differences between terms

• First difference: \(a_{2}-a_{1}=785 - 78=707\)
• Second difference: \(a_{3}-a_{2}=7855 - 785 = 7070\)
• Third difference: \(a_{4}-a_{3}=78555 - 7855=70700\)

Step3: Check if differences are constant

The differences \(707\), \(7070\), \(70700\) are not equal (they are increasing by a factor of 10 each time). So there is no common constant difference.

Answer:

No