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Olympiad workbook

Exam: Olympiad workbook
Subject: IOQM
Chapter: Sequences and Series

Olympiad workbook · IOQM · Sequences and Series

Five distinct 2-digit numbers are in a geometric progression. Find...

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

Correct answer

36

Step-by-step solution

Let the numbers be

\quad a \quad

ar

\quad a r^2 \quad a r^3 \quad a r^4

since all are 2 digit number

r=\frac{2}{3}

or

\frac{3}{2}

(as fourth power of integers greater than 3 are 3 digit numbers) Hence the five numbers are

(16,24,36,54,81)

Hence middle term is 36 .

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