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 10 cm, then for which of the following is not the value of n for which the area of Sn less 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 8Let an denote the length of a side of Sn. We are givenLength of a side of Sn= Length of a diagonal of Sn+1⇒an=√2an+1⇒an+1an=1√2Thus, a1,a2,a3,.... is a G.P. with first term 10 and common ratio 1√2.Therefore,an=10(1√2)n−1Also, Area (Sn)=a2n<1⇒[10(1√2)n−1]2<1⇒100<2n−1⇒ smallest possible value of n is 8.

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