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

If a,b,c are in GP, Prove that, `a(b^2+c^2) =c(a^2+b^2)`

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

If a,b,c,d are in GP then prove that, (a^2-b^2), (b^2-c^2), (c^2-d^2) are in GP.

If a, b, c are in GP then prove that, (a+2b+2c)(a-2b+2c)= a^2+ 4c^2

If a, b, c are in G.P., show that a^(2)b^(2)c^(2)((1)/(a^(3))+(1)/(b^(3))+(1)/(c^(3))) = a^(3) + b^(3) + c^(3) .

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

If a,b,c,d be 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)=(a b+b c+c d)^2 .

CENGAGE PUBLICATION-SEQUENCES AND SERIES-All Questions
  1. IF a(1),a(2),a(3),"...."a(10) be in AP and h(1),h(2),h(3),"...."h(10) ...

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  2. The harmonic mean of the roots of the equation (5+sqrt(2))x^2-(4+sqrt(...

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  3. If a,b,c are in GP, Prove that, a(b^2+c^2) =c(a^2+b^2)

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  4. If l n(a+c),l n(a-c) and l n(a-2b+c) are in A.P., then (a) a ,b ,c ...

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  5. If a,b,c are in G.P., then the equations ax^2+2bx+c =0 and dx^2+2ex+f ...

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  6. Sum of the first n terms of the series 1/2+3/4+7/8+(15)/(16)+............

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  7. The third term of a geometric progression is 4. Then the product of t...

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  8. In triangle ABC medians AD and CE are drawn, if AD=5, angleDAC= pi/8 a...

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  9. If tk is the kth term of a G.P., then show that t(n - k), tn, t(n + k)...

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  10. If pth, qth, and rth term of an AP are equal to corresponding terms of...

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  11. Sum of 1/(sqrt(2)+sqrt(5))+1/(sqrt(5)+sqrt(8))+1/(sqrt(8)+sqrt(11))+1/...

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  12. If fourth term of an HP is 3/5 and its 8th term is 1/3 , then find it...

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

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  14. If a ,b ,c are in A.P., the a/(b c),1/c ,1/b will be in a. A.P b. G.P....

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  15. If (p^2+q^2), (pq+qr), (q^2+r^2) are in GP then Prove that p, q, r are...

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  16. The coefficient of the quadratic equation a x^2+(a+d)x+(a+2d)=0 are co...

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  17. Let S denote sum of the series 3/(2^3)+4/(2^4 .3)+5/(2^6 .3)+6/(2^7 .5...

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  18. Let the sum of first three terms of G.P. with real terms be 13/12 and ...

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  19. Given a,b,c are in A.P.,b,c,d are in G.P and c,d,e are in H.P .If a=2 ...

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  20. The terms a1,a2,a3 form an arithmetic sequence whose sum is 18.The ter...

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