GP and 2-digit number | PRMO 2017 | Question 16

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

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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