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If a ,b ,c are in A.P. and a^2, b^2, c^...

If `a ,b ,c` are in A.P. and `a^2, b^2, c^2` are in H.P., then prove that either `a=b=cora ,b ,-c/2` form a G.P.

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CENGAGE ENGLISH-SEQUENCES AND SERIES-All Questions
  1. .Let a1, a2,............ be positive real numbers in geometric progr...

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  2. about to only mathematics

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  3. If a ,b ,c are in A.P. and a^2, b^2, c^2 are in H.P., then prove tha...

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  4. Let a ,b be positive real numbers. If a, A1, A2, b be are in arithmeti...

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  5. The sum of an infinite G.P. is 57 and the sum of their cubes is 9747, ...

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  6. If a^2+b^2,a b+b c and b^2+c^2 are in G.P., then a ,b ,c are in a. A.P...

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  7. If y^2=x za n da^x=b^y=c^z , then prove that (log)6a=(log)c bdot

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  8. The geometric mean between -9 and -16 is 12 b. -12 c. -13 d. none of t...

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  9. The value of 0.2

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  10. If (1+a)(1+a^(2))(1+a^(4)) . . . . (1+a^(128))=underset(r=0)overset(n)...

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  11. The number of terms common between the series 1+2+4+8+ .......to 100 t...

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  12. After striking the floor, a certain ball rebounds (4/5)th of height ...

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  13. If S denotes the sum to infinity and Sn the sum of n terms of the seri...

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  14. The first term of an infinite geometric series is 21. The second term ...

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  15. Given that x+y+z=15 when a ,x ,y ,z ,b are in A.P. and 1/x+1/y+1/z=5/3...

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  16. Let a1,a2,a3…… ,an be in G.P such that 3a1+7a2 +3a3-4a5=0 Then common...

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  17. The consecutive digits of a three digit number are in G.P. If middle ...

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  18. If Sn=1^2-2^2+3^2-4^2+5^2-6^2+ ,t h e n S(40)=-820 b. S(2n)> S(2n+2) ...

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  19. If sum(r=1)^n r(r+1)(2r+3)=a n^4+b n^3+c n^2+d n+e , then (a) a-b=d-c ...

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  20. Find the sum off the terms of an infinite decreasing G.P. in which all...

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