Answer:
The sequence is geometric.
Step-by-step explanation:
In Arithmetic sequence, there is a common difference between any two consecutive terms but in Geometric sequence, there is a common ratio between any two consecutive terms.
Given sequence is: 50, -50, 50, -50,.................
Lets assume, the terms as [tex]a_{1}, a_{2}, a_{3}, a_{4},...........[/tex]
Checking for common difference:
[tex]a_{2}-a_{1}= (-50)-(50)= -100\\ \\ a_{3}-a_{2}=(50)-(-50)=100\\ \\ a_{4}-a_{3}=(-50)-(50)=-100[/tex]
As there is no common difference, so it's not an arithmetic sequence.
Checking for common ratio
[tex]\frac{a_{2}}{a_{1}}=\frac{-50}{50}=-1\\ \\ \frac{a_{3}}{a_{2}}=\frac{50}{-50}=-1\\ \\ \frac{a_{4}}{a_{3}}=\frac{-50}{50}=-1[/tex]
As there is a common ratio, so it's a geometric sequence.
