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NDA 2010
Exam
NDA
Year
2010
Subject
Mathematics
Chapter
Sequences and Series

NDA 2010 · Mathematics · Sequences and Series

A square is drawn by joining mid-point of the sides of a square....

A square is drawn by joining mid-point of the sides of a square. Another square is drawn inside the second square in the same way and the process is continued indefinitely. If the side of the first square is 16 cm then what is the sum of the areas of all the squares?

Options

  1. A256 sq. cm
  2. B512sq.cm512 \mathrm{sq}. \mathrm{cm}
  3. C1024 sq. cm
  4. D512/3512 / 3 sq. cm

Correct answer

B. 512sq.cm512 \mathrm{sq}. \mathrm{cm}

Step-by-step solution


Area of given square =256cm2=256 \mathrm{ cm}^2 Now length of square drawn by joining mid points =82cm∴=8 \sqrt{2} \mathrm{ cm}\therefore Area =128cm2=128 \mathrm{ cm}^2 Next area =64cm2=64 \mathrm{ cm}^2 And so on, Sum =256+128+64+32+…=256+128+64+32+\ldots which is in G.P  Sum =2561−12=256×2=512 sq. cm. \begin{aligned} & \text{ Sum }=\frac{256}{1-\frac{1}{2}}=256 \times 2 \\ & =512 \text{ sq. cm. } \end{aligned}
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