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If x ,y , and z are in G.P. and x+3,y+3,...

If `x ,y ,` and `z` are in G.P. and `x+3,y+3`, and `z+3` are in H.P., then a.`y=2` b. `y=3` c. `y=1` d. `y=0`

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If a^(x) = b^(y) = c^(z) and a, b, c, are in G.P., prove that x, y, z are in H.P.

If a, b, c be in A.P. and x, y, z be in G.P., prove that, x^(b-c).y^(c-a).z^(a-b) = 1 .

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 .

If a, b, c are in G.P. and a^(1/x) =b^(1/y)=c^(1/z) , prove that x, y , x are in A.P

If a,x,b are in A.P.,a,y,b are in G.P. and a,z,b are in H.P. such that x=9z and a>0, b>0, then (a) y=3z. (b) x=3y (c) 2y= x+z (d) none of these

If (y/z)^a.(z/x)^b.(x/y)^c=1 and a,b,c are in A.P ,show that x,y,z are in G.P.

If a, b, c are in G.P. and a^(1//x) = b^(1//y) = c^(1//z) , show that x, y, z are in A.P.

Given that x+y+z=15 when a ,x ,y ,z ,b are in A.P. and 1/x+1/y+1/z=5/3w h e na ,x ,y ,z ,b are in H.P. Then (i) G.M. of a and b is 3 (ii) One possible value of a+2b is 11 (iii) A.M. of a and b is 6 (iv) Greatest value of a-b is 8

If a,b,c are in A.P and x,y,z are in G.P prove that (b-c) logx+(c-a) log y+(a-b) log z=0

If x ,2y ,3z are in A.P., where the distinct numbers x ,y ,z are in G.P, then the common ratio of the G.P. is a. 3 b. 1/3 c. 2 d. 1/2

CENGAGE PUBLICATION-SEQUENCES AND SERIES-All Questions
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  2. If x ,y ,a n dz are distinct prime numbers, then (a).x , y , a n dz ma...

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  3. If x ,y , and z are in G.P. and x+3,y+3, and z+3 are in H.P., then a.y...

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

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

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

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

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

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

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  10. If the sum to infinity of the series 1+2r+3r^2+4r^3+ is 9/4, then val...

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  11. The sum o f series 1+4/5+7/(5^2)+(10)/(5^3)+oo is a. 7//16 b. 5//16 ...

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  12. The sum 20 terms of a series whose rth term is given by Tr=(-1)^r((r^2...

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  13. Consider the sequence 1,2,2,4,4,4,4,8,8,8,8,8,8,8,8,... Then 1025th te...

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  14. If the first term of an A.P. is – 18 and its 10th term is zero, then f...

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  15. Suppose that F(n + 1) =(2F(n) + 1)/2 for n = 1,2,3,,,, and F(1) = 2. T...

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  16. If the numbers n – 2, 4n – 1 and 5n + 2 are in A.P., find the value of...

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  17. The first and the last terms of an A.P. are 17 and 350 respectively. I...

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  18. If a ,b ,and c are in A.P., then a^3+c^3-8b^3 is equal to (a).2a b c (...

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  19. The number of terms of an A.P. is even. The sum of the odd terms is 24...

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  20. The first term of an A.P. is 5, the last term is 45 and the sum is 400...

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