Try this beautiful problem from American Invitational Mathematics Examination I, AIME I, 2009 based on geometric sequence.
Call a 3-digit number geometric if it has 3 distinct digits which, when read from left to right, form a geometric sequence. Find the difference between the largest and smallest geometric numbers.
Sequence
Series
Real Analysis
Answer: is 840.
AIME, 2009
Introduction to Real Analysis, 4th Edition by Robert G. Bartle, Donald R. Sherbert
3-digit sequence a, ar, \(ar^{2}\). The largest geometric number must have a<=9.
ar \(ar^{2}\) less than 9 r fraction less than 1 For a=9 is \(\frac{2}{3}\) then number 964.
a>=1 ar and \(ar^{2}\) greater than 1 r is 2 and number is 124. Then difference 964-124=840.
