Question

# Let S1,S2,...Sn be squares such that for each n≥1, the length of a side of Sn equals the length of the diagonal of Sn+1. If the length of a side of S1 is 10 cm, then the least value of n for which the area of Sn less that 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 B 8S1=10 cm, Area(Sn)<100 cm2 Length of Sn= length of diagonal of Sn+1 As we know, length of Sn=√2 length of side of Sn+1 ∴length of side Sn+1length of side Sn=length of side Snlength of side Sn−1=.....=length of side S2length of side S1=1√2 Therefore, S1,S2,S3......,Sn+1 are in GP ∴a=10,r=1√2 Sides of Sn=10(1√2)n−1=102(n−1)/2 Area =(102(n−1)/2)2<1

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