Triangular Numbers in Geometric Sequence

Theorem

The numbers:

$1, 6, 36$

are the smallest triangular numbers in geometric sequence.


Proof

\(\ds 6 \div 1\) \(=\) \(\ds 6\)
\(\ds 36 \div 6\) \(=\) \(\ds 6\)

Hence the common ratio is $6$.

$\blacksquare$


Sources

  • 1986: David Wells: Curious and Interesting Numbers ... (previous) ... (next): $36$
  • 1997: David Wells: Curious and Interesting Numbers (2nd ed.) ... (previous) ... (next): $36$
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