Finding Every Third Number and Returning the Largest of Them

Problem:

We want to scan List1 (Column A) for every third number and then determine which of them is the largest.

Solution:
Use the MAX, IF, MOD, and ROW functions as shown in the following Array formula:
{=MAX(IF(MOD(ROW($A$2:$A$10)-ROW($A$2)+1,3)=0,$A$2:$A$10))}