Find the general term of the arithmetical progression:

$$(1-\sqrt{2},1+\sqrt{2}, 1+3\sqrt{2}, 1+5\sqrt{2}, 1+7\sqrt{2}, \ldots)$$

### Development:

Let's see what the difference is $$$d=(1+\sqrt{2})-(1-\sqrt{2})=\sqrt{2}+\sqrt{2}=2\sqrt{2}$$$ And, as the first term is $$a_1=1-\sqrt{2}$$, we know that:

$$$a_n=(1-\sqrt{2})+(n-1)\cdot 2 \cdot \sqrt{2}$$$

Arranging this expression we have:

$$$a_n=(1-\sqrt{2})+2\sqrt{2}(n-1)=1-\sqrt{2}-2\sqrt{2}+2\sqrt{2}\cdot n=2\sqrt{2}n+1-3\sqrt{2}$$$

### Solution:

$$a_n=2\sqrt{2}n+1-3\sqrt{2}$$