Agrocery clerk sets up a display of oranges in the form of a triangle using 14 oranges at the base and 1 at the top how many oranges were used by the clerk to make the arrangement?

  105

Step-by-step explanation:

The numbers that can be used to form triangles are collectively called "triangle numbers." The n-th triangle number is the sum of all numbers less than or equal to n. It is ...

  n(n+1)/2

For n=14, the number is 14(15)/2 = 7·15 = 105.

The clerk used 105 oranges to make the arrangement.