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The side of a given square is equal to a...

The side of a given square is equal to a. The mid-points of its sides are joined to form a new square. Again, the mid-points of the sides of this new square are joined to form another square. This process is continued indefinitely. Find the sum of the areas of the squares and the sum of the perimeters of the squares.

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ICSE-SEQUENCE AND SERIES -CHAPTER TEST
  1. The side of a given square is equal to a. The mid-points of its sides ...

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  2. Write down the first five terms of the sequence, whose nth term is (-1...

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  3. If the 3rd and the 6th terms of an A.P. are 7 and 13 respectively, fin...

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  4. Find the sum of all natural numbers between 100 and 1000 which are mul...

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  5. How many terms of the A.P., -6,(-11)/(2),-5 ... are needed to give the...

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  6. Determine the sum of the first 35 terms of an A.P. if a(2), = 2 and a(...

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  7. If the first term of an A.P. is 2 and the sum of first five terms is e...

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  8. Insert 3 arithmetic means between 2 and 10.

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  9. Find 12th term of a G.P. whose 8th term is 192 and the common ratio is...

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  10. The first term of a G.P. is 1. The sum of the third and fifth terms is...

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  11. The sum of first three terms of a G.P. is (39)/(10) and their product ...

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  12. The sum of some terms of a G.P. is 315 whose first term and the common...

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  13. Find the sum of the series 0.6 +0.66 +0.666+ ... to the n terms

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  14. The sum of an infinite series is 15 and the sum of the squares of thes...

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  15. Insert three geometric means between 1 and 256.

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  16. In the sum to infinity of the series 3+(3+x) (1)/(4) + (3+2x)(1)/(4^(2...

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  17. Find the sum to n terms of the series 3.8 +6.11 +9.14 + ...

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  18. Find the sum 5^(2)+ 6^(2) + 7^(2) + ... + 20^(2).

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  19. If in a geometric progression consisting of positive terms, each term ...

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  20. If the first term of an infinite G.P. is 1 and each term is twice the ...

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  21. If fifth term of a G.P. is 2, then the product of its first 9 terms is

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