How to find the nth term of the series can anyone explain

1, 5, 13, 27, 48, 78, 118, 170, 235, 315, 411, 525, 658, 812, 988, 1188, 1413, 1665, …

It’s ans is n(n+2)(2n+1)/8 But how?

How to find the nth term of the series can anyone explain

1, 5, 13, 27, 48, 78, 118, 170, 235, 315, 411, 525, 658, 812, 988, 1188, 1413, 1665, …

It’s ans is n(n+2)(2n+1)/8 But how?

This sequence looks like the **Friedreich’s formula** for counting the number of triangles in a triangle which says,

If {T_n} represents number of Triangles in a triangle of n unit lengths, then,

{T_n} = \left \lfloor n(n+2)(2n+1)/8 \right \rfloor

A good derivation is given here.

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