Question

Which of the following is an arithmetic sequence? A. 1, 0, 1, 0, 1, 0, ...B. 800, 200, 50, ...C. 10, 7, 4, 1, -2, ...D. 1, 3, 9, 27,...

Answer 1

Given:

The sequences in options.

Required:

Which of the sequence is an arithmetic sequence.

Explanation:

The arithmetic sequence has a common ration, that is equal for every pair of number

$d=a_2-a_1,d=a_3-a_2$

Now, in option c

$\begin{gathered} d=7-10=-3 \\ d=4-7=-3 \\ d=1-4=-3 \end{gathered}$

So, common ratio is -3 and hence sequence is arithmetic sequence.

Answer:

So, option c is correct.