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If A(1),A(2),A(3) denote respectively th...

If `A_(1),A_(2),A_(3)` denote respectively the areas of an inscribed polygon of 2n sides , inscribed polygon of n sides and circumscribed poylgon of n sides ,then `A_(1),A_(2),A_(3)` are in

A

A.P.

B

G.P.

C

H.P.

D

none of these

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The correct Answer is:
B
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Let A_(1), A_(2), A_(3),….., A_(n) be squares such that for each n ge 1 the length of a side of A _(n) equals the length of a diagonal of A _(n+1). If the side of A_(1) be 20 units then the smallest value of 'n' for wheich area of A_(n) is less than 1.

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OBJECTIVE RD SHARMA-PROPERTIES OF TRIANGLES AND CIRCLES CONNECTED WITH THEM-Exercise
  1. If p(1), p(2),p(3) are respectively the perpendiculars from the vertic...

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  2. If in Delta ABC, 8R^(2) = a^(2) + b^(2) + c^(2), then the triangle ABC...

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  3. If A(1),A(2),A(3) denote respectively the areas of an inscribed polygo...

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  4. If the angles of a triangle are in A.P.with common difference equal 1/...

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  5. In a triangle ABC, A = 8, b = 10 and c = 12. What is the angle C equal...

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  6. If the sides a, b, c of a triangle ABC are the roots of the equation x...

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  7. The area of a !ABC is b^(2)-(c-a)^(2). Then ,tan B =

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  8. In a DeltaABC, Sin A /SinC = sin(A-B)/ sin(B - C) , then a^2, b^2, c^2...

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  9. If in a triangle ABC, 3 sin A = 6 sin B=2sqrt3sin C, then the angle A...

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  10. The side of a Delta are in AP. And its area is 3/5xx (area of an equil...

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  11. In a triangle sin^(4)A + sin^(4)B + sin^(4)C = sin^(2)B sin^(2)C + 2si...

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  12. In any triangle ABC ,(tanA/2-tanB/2)/(tanA/2+tanB/2) is equal to

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  13. If the sides a,b and c of a !ABC are in A.P.,then (tanA/2+tanC/2):co...

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  14. If the sides of the triangle are the roots of the equation x^(3)-2x^(...

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  15. If AD, BE and CF are the medians of a ABC ,then (AD^(2)+BE^(2)+CF^(2))...

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  16. If a DeltaABC is right angled at B, then the diameter of the incircle ...

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  17. If a^(2),b^(2),c^(2) are in A.P.,then which of the following is also i...

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  18. If in a !ABC , sin^(3)A+sin^(3)B+sin^(3)C=3sinAsinBsinC, then abs(...

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  19. If the ex-radii of a triangle are in H.P.,then the corresponding sides...

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  20. If I is the incentre of a !ABC , then IA:IB:IC is equal to

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