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Question

Let S1,S2,..... be squares such that for each n1, the length of a side of Sn equals the length of a diagonal of Sn+1. If the length of a side of S1 is 10cm, then for which of the following values of n is the area of Sn less then 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 options are
B 8
C 9
D 10
Given xn=xn+12
x1=x22,x2=x32,xn=xn+12
On multiplying x1=xn+1(2)nxn+1=x1(2)n
Hence xn=x1(2)n1
Area of Sn=x2n=x212n1<12n1>x21(x1=10)
2n1>100
But 27>100,28>100, etc.
n1=7,8,9....n=8,9,10.....

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