Question

reClassify the sequence (4.) = {1,24,5,28,...) as arithmetic, geometric, or neither. If there is not enough information to classify the sequence, choose not enoughnformationO A arithmeticOB. geometricOC neitherOD. not enough information

Answer 1

An arithmetic sequence is a sequence of numbers in which each successive term increases or decreases by a constant value, called the common difference.

A geometric sequence is one in which each successive term of the series is obtained by multiplying the previous term by a constant value called the common ratio.

In the series below:

`\mleft\lbrace a_n\mright\rbrace\text{ = }\mleft\lbrace1,\text{ 24, 5, 28,}\ldots\mright\rbrace`

first term = 1

second term = 24

third term = 5

fourth term = 28

Common difference d:

The difference between the second and first terms must be equal to the difference between the third and the second term.

`\begin{gathered} d\text{ = second term - first term} \\ =\text{ 24 -1} \\ d\text{ = 23} \end{gathered}`
`\begin{gathered} d\text{ = third term - second term} \\ =5-24 \\ d\text{ = -19} \end{gathered}`

Since the common differences obtained above are not equal, the sequence is thus not an arithmetic sequence.

Common ratio r:

The common ratio between the second and the first term must be equal to the common ratio between the third and the second term.

`\begin{gathered} r\text{ = }\frac{\sec ond\text{ term}}{first\text{ term}} \\ =(24)/(1) \\ \Rightarrow r=24 \end{gathered}`
`\begin{gathered} r=\frac{third\text{ term}}{\sec ond\text{ term}} \\ =(5)/(24) \\ \Rightarrow r=0.208 \end{gathered}`

Since the common ratios obtained above are not equal, the sequence is thus not a geometric sequence.

Hence, the sequence is neither an arithmetic sequence nor a geometric sequence.

The correct option is C.