The correct sequence in which the lengths of the following units increase is 1, 3, 2.

1. The Angstrom is the smallest unit of length, equal to 0.1 nanometer. It is used to measure atomic distances and sizes.

2. The Nanometer is the second smallest unit of length and is equal to one billionth of a meter. It is commonly used in fields like nanotechnology and biology to measure the size of molecules and nanoparticles.

3. The Micron is the largest unit of the three and is equal to one millionth of a meter. It is often used to measure the size of small objects like cells, bacteria, and dust particles.

Therefore, the correct sequence is 1, 3, 2, as the Angstrom is smaller than the Nanometer, and the Nanometer is smaller than the Micron.

Note: The provided answer is correct.