Let A₁, A₂, A₃,………. be squares such that for each $n \geq 1,$ the length of the side of A_n equals the length of diagonal of A_n+1. If the length of A₁ is 12cm then smallest value of an for which area of A_n is less than one, is………………….

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alok kumar singh | Contributor-Level 10

a month ago

Let a_n be the side of square A_n

$a_{n} = \sqrt[]{2} a_{n + 1}$

a₁ = 12

a_n = 12 $\times {(\frac{1}{\sqrt[]{2}})}^{n - 1}$

${(a_{n})}^{2} < 1$

$\frac{144}{2^{(n - 1)}} < 1$

$\Rightarrow 2^{(n - 1)} > 144$

$\Rightarrow n - 1 \geq 8$

$\Rightarrow n \geq 9$

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Let A₁, A₂, A₃,………. be squares such that for each $n \geq 1,$ the length of the side of A_n equals the length of diagonal of A_n+1. If the length of A₁ is 12cm then smallest value of an for which area of A_n is less than one, is………………….

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

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Let A₁, A₂, A₃,………. be squares such that for each $n \geq 1,$ the length of the side of A_n equals the length of diagonal of A_n+1. If the length of A₁ is 12cm then smallest value of an for which area of A_n is less than one, is………………….