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QJEEM21Ma9e50: JEE Main 2021 Mathematics - Class 11 JEEM21Ma9e50 Solution: Let A 1 , A 2 , A 3 , ....... be squares such that for each n…

Let A1, A2, A3, ....... be squares such that for each n ≥\ge 1, the length of the side of An equals the length of diagonal of An+1. If the length of A1 is 12 cm, then the smallest value of n for which area of An is less than one, is __________.

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JEE Main 2021 (Online) 25th February Morning Shift Mathematics - Sequences and Series Question 159 English Explanation

∴\therefore Side lengths are in G.P.

Tn=12(2)n−1{T_n} = {{12} \over {{{\left( {\sqrt 2 } \right)}^{n - 1}}}}

∴\therefore Area =1442n−1= {{144} \over {{2^{n - 1}} }} < 1

\Rightarrow {2^{n - 1}} &gt; 144

Smallest n = 9

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