Question

What is the common difference in the following arithmetic sequence?

3/4, 6/4, 9/4
, . . .

(1 point)
The common difference in the arithmetic sequence is
.

Answer 1

To find the common difference in the arithmetic sequence, you can subtract any term from the subsequent term.

Let's calculate it:

The second term is \( \frac{6}{4} \) and the first term is \( \frac{3}{4} \):
\[
d = \frac{6}{4} - \frac{3}{4} = \frac{6 - 3}{4} = \frac{3}{4}
\]

Next, let's verify with the third term:
The third term is \( \frac{9}{4} \):
\[
d = \frac{9}{4} - \frac{6}{4} = \frac{9 - 6}{4} = \frac{3}{4}
\]

Since both calculations yield the same difference, the common difference in the arithmetic sequence is:
\[
\frac{3}{4}
\]

So, the common difference in the arithmetic sequence is \( \frac{3}{4} \).