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

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

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CENGAGE PUBLICATION-SEQUENCES AND SERIES-All Questions
  1. If the pth, qth, and rth terms of an A.P. are in G.P., then the common...

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  2. In a G.P. the first, third, and fifth terms may be considered as the ...

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

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  4. If the pth, qth, rth, and sth terms of an A.P. are in G.P., then p-q ,...

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  5. A B C is a right-angled triangle in which /B=90^0 and B C=adot If n po...

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  6. If (1-p)(1+3x+9x^2+27 x^3+81 x^4+243 x^5)=1-p^6,p!=1 , then the value ...

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  7. ABCD is a square of length a, a in N, a > 1. Let L1, L2 , L3... be poi...

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  9. If (1+3+5++p)+(1+3+5++q)=(1+3+5++r) where each set of parentheses cont...

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  10. If a x^3+b x^2+c x+d is divisible by a x^2+c ,t h e na ,b ,c ,d are in...

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  11. If the lines 3x + by + 5 = 0 and ax – 5y + 7 = 0 are perpendicular to ...

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  12. In a geometric series, the first term is a and common ratio is rdot If...

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  13. If x ,y ,a n dz are distinct prime numbers, then (a).x , y , a n dz ma...

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  15. If A.M., G.M., and H.M. of the first and last terms of the series of 1...

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  16. The sum 1+3+7+15+31+...to100 terms is a. 2^(100)-102 b. 2^(99)-101 c...

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  17. The sum of first 15 terms of an A.P. is 750 and its first term is 15. ...

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  18. The coefficient of x^(49) in the product (x-1)(x-3)(x-99)i s a. -99^...

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  19. Let S=4/(19)+(44)/(19^2)+(444)/(19^3)+ u ptooo . Then s is equal to a....

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  20. If Hn=1+1/2+...+1/ndot , then the value of Sn=1+3/2+5/3+...+(99)/(50) ...

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