    Question

# Let S1,S2,..... be squares such that for each n≥1, 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 10Given 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. ∴n−1=7,8,9....⇒n=8,9,10.....  Suggest Corrections  0      Similar questions
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