Question

Which of the following is true regarding the sequence below?

Answer 1

Answer:

A.The sequence is arithmetic because there is a common difference of $-\frac{5}{12}$

Step-by-step explanation:

We are given that a sequence

$\frac{7}{12}, \frac{1}{6},-\frac{1}{4},-\frac{2}{3}$

$a_1=\frac{7}{12}$

$a_2=\frac{1}{6}$

$a_3=-\frac{1}{4}, a_4=-\frac{2}{3}$

$a_2-a_1=\frac{1}{6}-\frac{7}{12}=\frac{2-7}{12}=-\frac{5}{12}$

$a_3-a_2=\frac{-1}{4}-\frac{1}{6}=\frac{-3-2}{12}=-\frac{5}{12}$

$a_4-a_3=\frac{-2}{3}+\frac{1}{4}=\frac{-8+3}{12}=-\frac{5}{12}$

The difference between consecutive terms are constant .When the difference between two consecutive terms is constant then the sequence is called arithmetic sequence.

Hence the given sequence is arithmetic sequence.

Answer:A.The sequence is arithmetic because there is a common difference of $-\frac{5}{12}$