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If a, b,c are in G.P., prove that the fo...

If a, b,c are in G.P., prove that the following are also in G.P. :
`a^(2),b^(2),c^(2) `.

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If a, b,c are in G.P., prove that the following are also in G.P. : a^(3),b^(3),c^(3) .

If a, b,c are in G.P., prove that the following are also in G.P. : a^(2)+b^(2),ab+bc,b^(2)+c^(2) .

If a, b, c are in A.P., prove that : b+c,c+a,a+ b are also in A.P.

If a,b,c, d are in G.P., show that : a+b,b+ c and c+d are also in G.P.

If a, b,c are in G.P, then log a, log b, log c are:

If a, b, c are in A.P., prove that : (bc)^-1,(ca)^-1 and (ab)^-1 are also in A.P.

If a, b, c are in A.P., then prove that : (a-c)^2 =4(b^2 -ac) .

If a, b, c are in A.P., prove that : a^3+4b^3+c^3=3b (a^2+c^2) .

If x,y,z are in G.P. and a^x= b^y=c^z , prove that log_b a. log_b c=1 .

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MODERN PUBLICATION-SEQUENCES AND SERIES-EXERCISE
  1. Find three numbers in G.P. : whose sum is 38 and whose product is 1728...

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  2. Find three numbers in G.P. whose sum is 35 and sum of their squares is...

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  3. If a, b,c are in G.P., prove that the following are also in G.P. : a...

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  4. If a, b,c are in G.P., prove that the following are also in G.P. : a...

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  5. If a, b,c are in G.P., prove that the following are also in G.P. : a...

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  6. If a,b,c, d are in G.P., show that : a+b,b+ c and c+d are also in G....

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  7. If a,b,c, d are in G.P., show that : a^(2)+b^(2), b^(2)+ c^(2) and c...

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  8. If a,b,c,d are in G.P., prove that (a^(n) + b^(n)), (b^(n) + c^(n)), (...

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  9. If a, b, c and d are in G.P. show that (a^2+ b^2+ c^2) (b^2 + c^2 + d^...

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  10. If a, b and c are three consecutive terms of an A.P.,prove that k^a, k...

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  11. If 1/(x+y),1/(2y),1/(y+z) are three consecutive terms of an A.P., prov...

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  12. The sum of four numbers in G.P. is 60 and the arithmetic mean of the f...

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  13. Find Soo, for the following infinite G.P.'s : 1,1/2, 1/2^2, ...........

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  14. Find Soo, for the following infinite G.P.'s : 1,1/3,1/9, ..............

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  15. Find Soo, for the following infinite G.P.'s : 5,20/7,80/49 , ..........

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  16. Find Soo, for the following infinite G.P.'s : 50, 42.5, 36.125, .....

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  17. Find Soo, for the following infinite G.P.'s : 0.3, 0.18, 0.108, ......

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  18. Sum the following series : (sqrt(2)+1)+1+(sqrt(2)-1)+ .......+oo.

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  19. Sum the following Series : 2/5+3/5^2+2/5^3+3/5^4+ .............. to...

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  20. The value of 9^(1/3), 9^(1/9).9^(1/27)…………..upto infty is:

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