AMO · 2027 · Grades 4-5 · Self-study SET 27 Question 2

Find the sum of the numbers in the 101st group: $(1,4,6),(2,6,10),(3,8,14),\ldots$. Continue the pattern in which the first, second and third entries increase by 1, 2 and 4 respectively.

Enter one whole number, without units.