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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.

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

Geometric Progression

2-digit number

Middle term

But try the problem first...

Answer: is 36.

Source

Suggested Reading

PRMO, 2017, Question 16

Elementary Algebra by Hall and Knight

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.

- https://www.cheenta.com/rational-number-and-integer-prmo-2019-question-9/
- https://www.youtube.com/watch?v=lBPFR9xequA

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