Hexagonal centred numbers
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 term of this sequence and then calculate the 25th term of this sequence.
The answer is 1801.
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1 solution
We can find the formula for the nth term by partitioning the hexagon into 3 rhombi, plus the central spot.
The nth term is therefore 3n.(n-1) + 1 and consequently the 25th term is 1801.