The number is 12. Along each horizontal line and each line parallel to a side of the tree, the differences between successive numbers form an arithmetic progression.

The lines meeting at the top are as follows:

Sequence | 12 | 13 | 15 | 18 | 22 | 27 | |||||
---|---|---|---|---|---|---|---|---|---|---|---|

Differences | 1 | 2 | 3 | 4 | 5 | ||||||

Sequence | 12 | 10 | 11 | 15 | 22 | 32 | |||||

Differences | -2 | 1 | 4 | 7 | 10 |