Question

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

Answer 1

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  $a_{1}, a_{2}, a_{3}, a_{4},...........$

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

$\frac{a_{2}}{a_{1}}=\frac{-50}{50}=-1\\ \\ \frac{a_{3}}{a_{2}}=\frac{50}{-50}=-1\\ \\ \frac{a_{4}}{a_{3}}=\frac{-50}{50}=-1$

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