Can you count all these oranges?

Discrete Mathematics Level 2

The oranges are arranged such that there is 1 top orange; the second top layer has 2 more oranges than the top; the third has 3 more oranges than the second, and so on. Forming a tetrahedron of oranges, these "tetrahedral" numbers of oranges run as a series, as shown above.

What is the value of the \(100^{\text{th}}\) term of this series?

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