A square is drawn by joining the mid points of the sides of a given square in the same way and this process continues indefinitely. If a side of the first square is 4 cm, determine the sum of the areas all the square.
A. 32 Cm2
B. 16 Cm2
C. 20 Cm2
D. 64 Cm2
E. None of these
Answer: Option A
Solution(By Examveda Team)
Side of the first square is 4 cm.side of second square = $$2\sqrt 2 {\kern 1pt} $$ cm.
Side of third square = 2 cm.
and so on, i.e. 4, 2, $$\sqrt 2 $$ , $$\sqrt 2 $$ , 1 ........
Thus, area of these square will be = 16, 8, 4, 2, 1, $$\frac{1}{2}$$ ..........
Hence, Sum of the area of first, second, third square
$$\eqalign{ & = 16 + 8 + 4 + 2 + 1 + {\kern 1pt} \,...... \cr & = {\frac{{16}}{{ {1 - {\frac{1}{2}} } }}} \cr & = 32\,{\kern 1pt} c{m^2} \cr} $$
Related Questions on Progressions
Find the first term of an AP whose 8th and 12th terms are respectively 39 and 59.
A. 5
B. 6
C. 4
D. 3
E. 7
The sum of the first 16 terms of an AP whose first term and third term are 5 and 15 respectively is
A. 600
B. 765
C. 640
D. 680
E. 690
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