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Question

# Let S1,S2..........Sn be squares such that for each n≥ 1, the length of a side of a side of Sn equals the length of a diagonal of Sn+1. If the length of a side of S1 is 10 cm, then which of the following values of n is not possible if the Area of Sn is more than 1 sq. cm.

A
7
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B
8
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C
9
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D
10
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Solution

## The correct option is A 7Given xn=xn+1√2 ∵ x1=x2√2,x2=x3√2,xn=xn+1√2 On multiplying x1=xn+1(√2)n⇒ xn+1=x1(√2)n Hence xn=x1(√2)n−1 Area of Sn=x2n=x212n−1< 1⇒ 2n−1> x21(x1=10) ∵ 2n−1>100 But 27>100,28>100, etc.23 ∵ n−1=7,8,9....⇒ n=8,9,10...​

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