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If a ,1/b ,a n d1/p ,q ,1/r from two ari...

If `a ,1/b ,a n d1/p ,q ,1/r` from two arithmetic progressions of the common difference, then `a ,q ,c` are in A.P. if `p ,b ,r` are in A.P. b. `1/p ,1/b ,1/r` are in A.P. c. `p ,b ,r` are in G.P. d. none of these

A

p,b,r are in A.P

B

`1/p,1/b,1/r are in A.P`

C

p,b,r are in G.P

D

none of these

Text Solution

Verified by Experts

The correct Answer is:
B
Since a,q and c are in A.P. so
2q=a+c
`rArr1/p+1/r=2/b`
`rArr1/p,1/b,1/r` are in A.P.
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CENGAGE-PROGRESSION AND SERIES-Exercise (Single)
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  2. If the sides of a right angled triangle are in A.P then the sines of t...

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  3. If a ,1/b ,a n d1/p ,q ,1/r from two arithmetic progressions of the co...

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

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  5. Consider an A. P .a1,a2,a3,..... such that a3+a5+a8 =11and a4+a2=-2 th...

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  6. If a(1),a(2),a(3),…. are in A.P., then a(p),a(q),q(r) are in A.P. if p...

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  7. Let alpha,beta in Rdot If alpha,beta^2 are the roots of quadratic equ...

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  8. If the sum of m terms of an A.P. is same as the sum of its n terms, th...

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  9. If Sn, denotes the sum of n terms of an A.P., then S(n+3)-3S(n+2)+3S(n...

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  10. The first term of an A.P. is a and the sum of first p terms is zero, s...

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  11. If Sn denotes the sum of first n terms of an A.P. and (S(3n)-S(n-1))/(...

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

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

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  14. Concentric circles of radii 1,2,3,. . . . ,100 c m are drawn. The inte...

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  15. If a1,a2,a3….a(2n+1) are in A.P then (a(2n+1)-a1)/(a(2n+1)+a1)+(a2n-...

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  16. If a(1), a(2), …..,a(n) are in A.P. with common difference d ne 0, the...

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  17. ABC is a right-angled triangle in which angleB=90^(@) and BC=a. If n p...

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  18. If a ,b, c ,d are in G.P, then (b-c)^2+(c-a)^2+(d-b)^2 is equal to

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  19. Let {tn} be a sequence of integers in G.P. in which t4: t6=1:4a n dt2+...

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  20. if x , 2y and 3z are in AP where the distinct numbers x, yand z ar...

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