Question

Which sequence is an arithmetic sequence200, 100,50,255,-1,-7,-13-5,15,-45,1355,8,13,21

Answer 1

the only arithemetic sequence on the list is;

`5,-1,-7,-13\ldots`

Step-by-step explanation:

An Arithemetic sequence is a sequence in which the difference between consecutive terms are constant. it has a common differnce.

`d=a_1-a_0=a_2-a_1=a_n-a_(n-1)`

Let us check to see if the difference between consecutive terms in the given sequence is constant.

`\begin{gathered} 200,100,50,25 \\ 100-200\\e50-100\\e25-50 \\ It\text{ is not an arithemetic sequence} \end{gathered}`
`\begin{gathered} 5,-1,-7,-13 \\ -1-5=-7-(-1)=-13-(-7)=-6 \\ It\text{ is an arithemetic sequence} \end{gathered}`
`\begin{gathered} -5,15,-45,135 \\ 15-(-5)\\e-45-15\\e135-(-45) \\ It\text{ is not an arithemetic sequence} \end{gathered}`
`\begin{gathered} 5,8,13,21 \\ 8-5\\e13-8\\e21-13 \\ It\text{ is not an arithemetic sequence} \end{gathered}`

Therefore, the only arithemetic sequence on the list is;

`5,-1,-7,-13\ldots`