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

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

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

If a, b, c are in G.P., show that a^(2) + b^(2), ab + bc and b^(2) + c^(2) are also in G.P.

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

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

If a, b, c, d are in A.P. and a, b, c, d are in G.P., show that a^(2) - d^(2) = 3(b^(2) - ad) .

If a, b, c are In A.P., then show that, a^(2)(b+c), b^(2)(c+a), c^(2)(a+b) are in A.P. (ab+bc+ca != 0)

If a,b, c are in GP, Prove that a^2, b^2 , c^2 are in GP.

If a, b, c are In A.P., then show that, (a+2b-c) (2b+c-a)(c+a-b) = 4abc

CHHAYA PUBLICATION-SEQUENCE AND SERIES-Exercise 9 C (Short Answer Type Questions)
  1. If a, b, c and d are in G.P., show that, (a-b)^(2), (b-c)^(2), (c-d)...

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

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

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

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  5. If three numbers a, b, c satisfy the relation (a^(2) + b^(2)) (b^(2) +...

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  6. If a, b, c are in geometric progression, then show that, (a^(2) + ab...

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  7. A boy saves 1 paisa the first day, 2 paise the second day, 4 paise the...

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  8. Shri A. K. Roy borrows Rs. 6000 to repay the amount with interest of R...

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  9. A man borrows Rs. 19682 without interest and agrees to repay the money...

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  10. The A.M. of two numbers is 15 and their G.M. is 12. Find the numbers.

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  11. If a, b, c are in G.P. and x, y be the A.M. between a, b and b, c resp...

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  12. If a, b, c are in G.P. and x, y be the A.M. between a, b and b, c resp...

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  13. If a, b, c be in A.P. and x, y, z be in G.P., prove that, x^(b-c).y^...

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  14. The sum of three numbers in G.P. is 70. If each of the two extremes be...

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  15. Let t(r) be the rth term of an A.P. If t(2), t(8) and t(32) are in G.P...

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  16. If p, q, r be in arithmetic progression, then show that the pth, qth a...

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  17. The nth term of a series is 3^(n) + 2n, find the sum of first n terms ...

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  18. If one arithmetic mean A and two geometric means p, q be inserted betw...

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  19. If A is the A.M. and G is the G.M. of two unequal positive real number...

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  20. Between two positive real numbers a and b, one arithmetic mean A and t...

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