Triangular Numbers in Geometric Sequence
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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): $36$