Let A1,A2,A3,......be squares such that for each n≥1, the length of the side of Anequals the length of diagonal of An+1. If the length of A1 is 12 cm, then the smallest value of n for which area of An is less than one, is_______.

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answer is 9.

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Detailed Solution

The lengths of the sides are 12,122,1222........ Since the area is less than one 122n−12<1⇒144≤2n−1⇒2n−1>144 it gives the possible value of n is 9