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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 7

Given xn=xn+12
x1=x22,x2=x32,xn=xn+12
On multiplying x1=xn+1(2)n xn+1=x1(2)n
Hence xn=x1(2)n1
Area of Sn=x2n=x212n1< 1 2n1> x21(x1=10)
2n1>100
But 27>100,28>100, etc.23
n1=7,8,9.... n=8,9,10...


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