Let S1,S2,S3,...be squares such that for each n≥1, the lenght of a side of Sn equals the length of a diagonal of Sn+1.If the length of a side of S1 is 10cm and the area of Sn<1sq.cm.The the value of n is
A
n>7
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B
n≥8
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C
n<7
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D
n≤8
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Solution
The correct options are An>7 Bn≥8
We have,length of a side of Sn=length of the diagonal of Sn+1
⇒length of a side of Sn=√2×length of a side of Sn+1
⇒lengthofasideofSn+1lengthofasideofSn=1√2 for all n≥1
⇒sides of S1,s2,S3,... form a G.P with common ratio 1√2 and the first term 10