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If a, b and c are three consecutive term...

If a, b and c are three consecutive terms of an A.P.,prove that `k^a, k^b` and `k^c` are three consecutive terms of a G.P. Assume k to be a non-zero real number.

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MODERN PUBLICATION-SEQUENCES AND SERIES-EXERCISE
  1. If a,b,c,d are in G.P., prove that (a^(n) + b^(n)), (b^(n) + c^(n)), (...

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

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

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

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

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

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

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

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

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

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

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

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  14. Given a G.P. with a= 729 and 7th term 64, determine S7.

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  15. The common ratio of a G.P. is -4/5 and the sum to infinity is 80/9. Fi...

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  16. Find Soo of G.P. whose first term is 28 and the fourth term is 4/49 .

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  17. The sum of an infinite number of terms of a G.P. is 15 and the sum of ...

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  18. Evaluate the following : 0. bar 45.

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  19. Evaluate the following : 1. bar 36.

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  20. Evaluate the following : 0.2 bar 35.

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