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If a^((1)/(x))= b^((1)/(y))= c^((1)/(z))...

If `a^((1)/(x))= b^((1)/(y))= c^((1)/(z))` and a,b,c are in G.P., prove that x,y,z are in A.P.

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ICSE-SEQUENCE AND SERIES -EXERCISE 14 (e)
  1. Find: (i) the 7th term of 2,4,8,... (ii) the 9th term of 1,(1)/(2),(1)...

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  2. The second term of a G.P. is 18 and the fifth term is 486. Find: (i)...

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  3. Find the value of x for which x +9,x-6, 4 are the first three terms of...

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  4. If 5, x, y, z, 405 are the first five terms of a geometric progression...

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  5. Insert 3 geometric means between 16 and 256.

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  6. Insert 5 geometric means between (1)/(3) and 243.

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  7. If the A.M. and G.M. between two numbers are respectively 17 and 8, fi...

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  8. The second, third and sixth terms of an A.P. are consecutive terms of ...

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  9. The 5th, 8th and 11th terms of a G.P. are P, Q and S respectively. Sho...

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  10. The (p+q)th term and (p-q)th terms of a G.P. are a and b respectively....

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  11. If the pth, th, rth terms of a G.P. are x, y, z respectively, prove th...

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  12. In a set of four numbers, the first three are in G.P. and the last thr...

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  13. If a^((1)/(x))= b^((1)/(y))= c^((1)/(z)) and a,b,c are in G.P., prove ...

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  14. If one G.M., G and two A.M's p and q be inserted between two given num...

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  15. Construct a quadratic equation in x such that the A.M. of its roots is...

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  16. The fourth term of a G.P. is greater than the first term, which is pos...

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  17. The first, eighth and twenty-second terms of an A.P. are three consecu...

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