In many of the standard textbooks discussing Real Numbers, the Cauchy sequence that converges to $\sqrt{2}$ is given as

1, 1.4, 1.41, 1.414, 1.4142, ...

or

2, 1.5, 1.42, 1.415, 1.4143, ...

My question is how are these sequences generated? In other words, if I have 1, 1.4, 1.41 how do I figure out that the next element of the sequence is 1.414?