Try this beautiful problem from the Pre-RMO, 2017 based on GP and 2-digit number.
Five distinct 2-digit numbers are in geometric progression. Find the middle term.
Geometric Progression
2-digit number
Middle term
Answer: is 36.
PRMO, 2017, Question 16
Elementary Algebra by Hall and Knight
Let the numbers be \(a, ar, ar^{2}, ar^{3}, ar^{4}\)
for all are two digit number r=\(\frac{2}{3}\) or \(\frac{3}{2}\)
where fourth power of integers greater than 3 are 3 digit numbers
then five numbers (16,24,36,54,81)
then middle term=36.
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