Question

Which of the following is an arithmetic sequence?

Answer 1

Answer:

Step-by-step explanation:

The given above is an arithmetic sequence with first term equal to 3 and the common difference equal to 4. That is from 7 - 3 = 11 - 7 = 15 - 11. The nth term of an arithmetic sequence is given by the equation,

                                       an = a1 + (n - 1) x d

Substituting the given,

                                       an = 3 + 4(n - 1)

thus, the answer is the fourth choice. 

Answer 2

Option C is the correct answer.

Step-by-step explanation:

Option A:

        $\texttt{Term 2 - Term 1 = }\frac{6}{11}-\left ( -\frac{7}{11}\right )=\frac{13}{11}\\\\\texttt{Term 3 - Term 2 = }-\frac{5}{11}-\frac{6}{11}=-\frac{11}{11}$

Common difference is not same, not an arithmetic sequence.

Option B:

        $\texttt{Term 2 - Term 1 = }-\frac{3}{5}-\left ( -\frac{3}{4}\right )=\frac{3}{4}-\frac{3}{5}=\frac{3}{20}\\\\\texttt{Term 3 - Term 2 = }-\frac{3}{6}-\left ( -\frac{3}{5}\right )=\frac{3}{5}-\frac{3}{6}=\frac{3}{30}=\frac{1}{10}$

Common difference is not same, not an arithmetic sequence.

Option C:

        $\texttt{Term 2 - Term 1 = }2-\frac{1}{2}=\frac{3}{2}\\\\\texttt{Term 3 - Term 2 = }\frac{7}{2}-2=\frac{3}{2}\\\\\texttt{Term 4 - Term 3 = }5-\frac{7}{2}=\frac{3}{2}$

Common difference is same, an arithmetic sequence.

Option D:

         $\texttt{Term 2 - Term 1 = }-\frac{3}{2}-\frac{3}{4}=-\frac{18}{8}=-\frac{9}{4}\\\\\texttt{Term 3 - Term 2 = }3-\left ( -\frac{3}{2}\right )=\frac{9}{2}$

Common difference is not same, not an arithmetic sequence.

Option C is the correct answer.