What value of k causes the terms 6, 4k, 26 to form an arithmetic sequence?

k = 4.

Step-by-step explanation:

If it is arithmetic then the differences between consecutive terms will be equal, so:

4k - 6 = 26 - 4k

4k + 4k = 26 + 6

8k = 32

k = 32/8

k = 4.

There are 3 values given,

Find the difference between the first and last values:

26 - 6 = 20

Divide that by 2:

20 / 2 = 10

The difference between each number needs to be 10, so adding 10 to the first number would be 6 + 10 = 16

Now 4k = 16

Divide both sides by 4:

k = 16/4

k = 4