Question

Find the common difference of the arithmetic sequence shown.

Answer 1

Answer:

Option B is correct.

The common difference of the arithmetic sequence is, $\frac{1}{8}$

Step-by-step explanation:

Common difference(d) states that take any pair of successive numbers, and subtract the first from the second.

Given the arithmetic sequence:

1/4 ,  3/8,   1/2...

⇒$(a_1)$ = 1/4, $a_2 = \frac{3}{8}$ ,  $a_3 = \frac{1}{2}$ and so on..

By definition of common difference

$a_2 -a_1 = \frac{3}{8}-\frac{1}{4} = \frac{3-2}{8} = \frac{1}{8}$

$a_3 -a_2= \frac{1}{2}-\frac{3}{8} = \frac{4-3}{8} = \frac{1}{8}$  and so on..

⇒$d = a_2-a_1 = a_3-a_2=.....= \frac{1}{8}$

Therefore, the common difference of the arithmetic sequence is, $\frac{1}{8}$

Answer 2

Answer:

1/8

Step-by-step explanation:

To find the common difference, subtract the first term (1/4) from the second term (3/8); it's 1/8.  Notice that if you subtract 3/8 from 1/2 as a check, you obtain 1/8 again.