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If a,b,c are in A.P., then a^(3)+c^(3)-8...

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

A

2 abc

B

3abc

C

4abc

D

`-6 abc `

Text Solution

Verified by Experts

The correct Answer is:
D
2b=a+c
`rArr8b^(3)=(a+c)^(3)=a^(3)+c^(3)+3ac(a+c)`
or `8b^(3)=a^(3)+c^(3)+3ac(2b)`
or `a^(3)+c^(3)-8b^(3)=-6abc`
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CENGAGE-PROGRESSION AND SERIES-Exercise (Single)
  1. If a,b,c are in A.P., then a^(3)+c^(3)-8b^(3) is equal to

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  2. If three positive real numbers a,b,c are in AP such that abc=4, then t...

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  3. If log(2)(5.2^(x)+1),log(4)(2^(1-x)+1) and 1 are in A.P,then x equals

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  4. The largest term common to the sequences 1, 11 , 21 , 31 , to100 term...

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  5. In any A.P. if sum of first six terms is 5 times the sum of next six t...

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  6. If the sides of a right angled triangle are in A.P then the sines of t...

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

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

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

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

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

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

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

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

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

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

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

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