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If a,b and c are A.P. whereas x,y and z ...

If a,b and c are A.P. whereas x,y and z are in G.P. :
Prove that : `x^(b-c)*y^(c-a)*z^(a-b)=1`.

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ICSE-GEOMETRIC PROGRESSION -Exercise 11(D)
  1. If a,b and c are A.P. whereas x,y and z are in G.P. : Prove that : x...

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  2. Find the sum of G.P. : 1+3+9+27+ . . . . .. . to 12 terms.

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  3. Find the sum of G.P. : 0*3+0*03+0*003+0*0003+ . . . . . . . to 8 ter...

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  4. Find the sum of G.P. : 1-(1)/(2)+(1)/(4)-(1)/(8)+ . . . .. . . .. . ...

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  5. Find the sum of G.P. : 1-(1)/(3)+(1)/(3^(2))-(1)/(3^(3))+ . . . .. ....

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  6. Find the sum of G.P. : (x+y)/(x-y)+1+(x-y)/(x+y)+ . . . . .. . . . ...

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  7. Find the sum of G.P. : sqrt(3)+(1)/(sqrt(3))+(1)/(3sqrt(3))+ . . . ....

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  8. How many terms of the geometric progression 1+4+16+64+ . . . . .. . . ...

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  9. If the first term of a G.P is 27 and 8th term is 1/81, then the sum of...

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  10. A boy spends Rs. 10 on first day, Rs. 20 on second day, Rs. 40 on thir...

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  11. The 4^(th) and the 7^(th) terms of a G.P. are (1)/(27) and (1)/(729) r...

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  12. A geometric progression has common ratio = 3 and last term = 486. If t...

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  13. Find the sum of G.P. : 3,6,12, . . . . . . . . ., 1536.

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  14. How many terms of the series 2+6+18+ . . . . . . . . . . . Must be tak...

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  15. In a G.P., the ratio between the sum of first three terms and that of ...

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  16. How many terms of the G.P. (2)/(9),-(1)/(3),(1)/(2), . . . . . . . ....

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  17. If the sum of 1+2+2^(2)+ . . . . . . . . . .+2^(n-1) is 255, find the ...

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  18. Find the geometric mean between : (4)/(9) and (9)/(4)

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  19. Find the geometric mean between : 14 and (7)/(32)

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  20. Find the geometric mean between : 2a and 8a^(3)

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  21. The sum of three numbers in G.P. is (39)/(10) and their product is 1. ...

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