Question

Identify the sequence as arithmetic, geometric, both, or neither. 50, –50, 50, –50, . . . both arithmetic geometric neither description

Answer 1

The sequence is geometric.

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
`a_(1), a_(2), a_(3), a_(4),...........`

Checking for common difference:

`a_(2)-a_(1)= (-50)-(50)= -100\\ \\ a_(3)-a_(2)=(50)-(-50)=100\\ \\ a_(4)-a_(3)=(-50)-(50)=-100`

As there is no common difference, so it's not an arithmetic sequence.

Checking for common ratio

`(a_(2))/(a_(1))=(-50)/(50)=-1\\ \\ (a_(3))/(a_(2))=(50)/(-50)=-1\\ \\ (a_(4))/(a_(3))=(-50)/(50)=-1`

As there is a common ratio, so it's a geometric sequence.