Question

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

Answer 1

Answer:

the only arithemetic sequence on the list is;

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

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\ne50-100\ne25-50 \\ 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)\ne-45-15\ne135-(-45) \\ It\text{ is not an arithemetic sequence} \end{gathered}$$\begin{gathered} 5,8,13,21 \\ 8-5\ne13-8\ne21-13 \\ It\text{ is not an arithemetic sequence} \end{gathered}$

Therefore, the only arithemetic sequence on the list is;

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