Try this beautiful problem from the Pre-RMO, 2017 based on GP and 2-digit number.

GP and 2-digit number – PRMO 2017


Five distinct 2-digit numbers are in geometric progression. Find the middle term.

  • is 107
  • is 36
  • is 840
  • cannot be determined from the given information

Key Concepts


Geometric Progression

2-digit number

Middle term

Check the Answer


But try the problem first…

Answer: is 36.

Source
Suggested Reading

PRMO, 2017, Question 16

Elementary Algebra by Hall and Knight

Try with Hints


First hint

Let the numbers be \(a, ar, ar^{2}, ar^{3}, ar^{4}\)

for all are two digit number r=\(\frac{2}{3}\) or \(\frac{3}{2}\)

Second Hint

where fourth power of integers greater than 3 are 3 digit numbers

Final Step

then five numbers (16,24,36,54,81)

then middle term=36.

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