JEE MAIN - Mathematics (2021 - 25th February Morning Shift - No. 18)
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 __________.
Answer
9
Explanation
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$$ \therefore $$ Side lengths are in G.P.
$${T_n} = {{12} \over {{{\left( {\sqrt 2 } \right)}^{n - 1}}}}$$
$$ \therefore $$ Area $$ = {{144} \over {{2^{n - 1}} }}$$ < 1
$$ \Rightarrow {2^{n - 1}} > 144$$
Smallest n = 9
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