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If a, b a n d c are in A.P., a x ,b y ,a...

If `a, b a n d c` are in A.P., `a x ,b y ,a n dc z` in G.P. and `x,y,z` in H.P. then prove that `x/z+z/x=a/c+c/a` .

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CENGAGE PUBLICATION-SEQUENCES AND SERIES-All Questions
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  2. Find the number of terms in the series 20 ,19 1/3,18 2/3... the sum of...

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  3. If a, b a n d c are in A.P., a x ,b y ,a n dc z in G.P. and x,y,z in H...

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  4. Find the sum of all three-digit natural numbers, which are divisible b...

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  5. If a ,b ,c ,and d are in H.P., then find the value of (a^(-2)-d^-2)/(b...

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  6. Prove that a sequence in an A.P., if the sum of its n terms is of the ...

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  7. The product of the three numbers in G.P. is 125 and sum of their pr...

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  8. If the sequence a1, a2, a3,....... an ,dot forms an A.P., then prove ...

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  9. Find the value of n so that (a^(n+1)+b^(n+1))/(a^n+b^n) may be the g...

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  10. Three non-zero numbers a ,b , c are in A.P. Increasing a by 1 or incre...

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  11. A G.P. consists of an even number of terms. If the sum of all the t...

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  12. 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 ...

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  13. If the sum of n terms of a G.P. is 3-(3^(n+1))/(4^(2n)) , then find ...

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  14. Which term of the G.P. 2,1, 1/2,1/4, i s1/(128)?

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  15. 'n' A.M's are inserted between a and 2b, and then between 2a and b. If...

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  16. If (a^n+b^n)/(a^(n-1)+b^(n-1)) is the A.M. between a and b, then find ...

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  17. The first and second terms of a G.P. are x^(-4) and x^n , respectively...

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  18. If (a+b x)/(a-b x)=(b+c x)/(b-c x)=(c+dx)/(c-dx)(x!=0), then show t...

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  19. If n arithmetic means are inserted between 2 and 38, then the sum of t...

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  20. The first terms of  a G.P. is 1. The sum of the third and fifth ter...

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