Hexagonal centred numbers

Geometry Level 2

From the figure shown, hexagonal centered numbers which result from counting the number of spots making up a full hexagon, have the following sequence:

1, 7, 19, 37, 61, 91, 127, 169, 217, 271, 331 ...

Find an expression for the \( n^\text{th} \) term of this sequence and then calculate the 25th term of this sequence.

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