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

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

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If a,b,c,d are in G.P., prove that (a^(n) + b^(n)), (b^(n) + c^(n)), (c^(n) + d^(n)) are in G.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 and d are in G.P. show that (a^2+ b^2+ c^2) (b^2 + c^2 + d^2)= ( ab + bc + cd)^2 .

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

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If b^2+c^2, c^2+a^2, a^2+b^2 are in A.P. prove that : 1/(b + c), 1/(c + a), 1/(a + b) are also in A.P.

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MODERN PUBLICATION-SEQUENCES AND SERIES-EXERCISE
  1. If a, b,c are in G.P., prove that the following are also in G.P. : a...

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  2. 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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  3. 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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  4. If a,b,c,d are in G.P., prove that (a^(n) + b^(n)), (b^(n) + c^(n)), (...

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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