Question

Find the common difference of the arithmetic sequence shown.


1/4,,,3/8,,,1/2,,.....

1/16
1/8
1/4

, , , ...

Answer 1

1/16?????

Answer 2

\[\Huge \frac{3}{8}-\frac{1}{4}=\]

Answer 3

I would say 5/8 but that doesn't seem to be a choice. Because if you make all of them with 8 on the bottom they seem to go up one 8th per step

Answer 4

We need to find d, the distance between each sequence:
$$\frac{1}{4} + (n-1)d=a_n\text{ where, n=1,2,...}$$
So take $$a_n=\frac{3}{8}$$
$$\frac{1}{4}+(4-1)d=\frac{3}{8}\text{ then d = }\frac{1}{24}$$
We used n=4 because it's the 4th element in the sequence.

So d=\(\dfrac{1}{24}\) is your answer.

Answer 5

You could have also used n=7 for \(a_7=\frac{1}{2}\) to find d, and would have found the same answer.

Answer 6

The formula for the arithmetic sequence I used above is documented here: http://en.wikipedia.org/wiki/Arithmetic_sequence