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.
Step-by-step explanation:
Option A:
[tex]\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}[/tex]
Common difference is not same, not an arithmetic sequence.
Option B:
[tex]\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}[/tex]
Common difference is not same, not an arithmetic sequence.
Option C:
[tex]\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}[/tex]
Common difference is same, an arithmetic sequence.
Option D:
[tex]\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}[/tex]
Common difference is not same, not an arithmetic sequence.
Option C is the correct answer.
