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If one geometric mean G and two arithmet...

If one geometric mean `G` and two arithmetic means `A_1a n dA_2` be inserted between two given quantities, prove that `G^2=(2A_1-A_2)(2A_2-A_1)dot`

A

a + b

B

ab

C

`(ab)/(a+b)`

D

`(a)/(b)`

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AAKASH INSTITUTE ENGLISH-SEQUENCES AND SERIES -Assignment (SECTION - A) One option is correct
  1. If the first, second and last term of an A.P. are a ,\ b and 2a res...

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  2. Sum of first n terms of an A.P. whose last term is l and common dif...

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  3. If one geometric mean G and two arithmetic means A1a n dA2 be inserted...

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  4. The fourth term of the G.P. 4, - 2 , 1 , … is

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  5. Find: n th term of the G.P. sqrt(3),1/(sqrt(3)),1/(3sqrt(3)),

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  6. Which term of the progression 18 ,-12 ,8, i s(512)/(729)?

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  7. The third term of a G.P. is 3. Find the product of its first five term...

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  8. If (a^n+b^n)/(a^(n-1)+b^(n-1))is the A.M. between a and b, then find t...

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  9. If (2p)th term of a G.P is q^2 and (2q)th term is p^2 then (p+q)th ter...

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  10. Three number whose product it 512 are in G.P. If 8 is added to the f...

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  11. If first and eightth terms of a G.P. are x^(-4) and x^(52) and it...

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  12. Find the sum of first n term of a G.P.1+(1)/(2)+(1)/(4)+(1)/(8)+...

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  13. The n^(th) term of a GP is 128 and the sum of its n terms is 255. If i...

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  14. How many terms of the series 1+3+9+ .. .........sum to 364?

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  15. If the (p+q)^(th) term of a G.P. is a and (p-q)^(th) term is b, determ...

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  16. If the sum of three numbers in a GP. is 26 and the sum of products tak...

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  17. If a,b,c are in G.P then (b-a)/(b-c)+(b+a)/(b+c)=

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  18. If x ,2x+2 and 3x+3 are the first three terms of a G.P., then the four...

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  19. If g(1) , g(2) , g(3) are three geometric means between two positi...

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  20. The fifth term of a G.P. is 32 and common ratio is 2 , then the su...

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