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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

values of n is the area of Sn greater then 1sq 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


(b, c, d) Given xn = xn+1 2

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 = x2n2n1 < 1 ⇒ 2n1 > x21 (x1 = 10)

2n1 > 100

But 27 > 100, 28>100, etc.

∴ n - 1 = 7, 8, 9....... ⇒ n = 8, 9, 10.........


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