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Let a ,b >0, let 5a-b ,2a+b ,a+2b be in ...

Let `a ,b >0,` let `5a-b ,2a+b ,a+2b` be in A.P. and `(b+1)^2, a b+1,(a-1)^2` are in G.P., then the value of `(a^(-1)+b^(-1))` is _______.

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CENGAGE PUBLICATION-SEQUENCES AND SERIES-All Questions
  1. If tn denotes the nth term of the series 2+3+6+11+18+...then t(50)...

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  2. The number of positive integral ordered pairs of (a ,b) such that 6,a ...

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  3. Let a ,b >0, let 5a-b ,2a+b ,a+2b be in A.P. and (b+1)^2, a b+1,(a-1)^...

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  4. The difference between the sum of the first k terms of the series ...

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  5. The value of the sum(n=0)^oo(2n+3)/(3^n) is equal to.

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  6. How many two digit numbers are divisible by 3 ?

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  7. If the roots of 10 x^3-n x^2-54 x-27=0 are in harmonic progression...

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  8. The 5th and 8th terms of a geometric sequence of real numbers are 7! ...

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  9. Find the 31st term of an A.P. whose 11th term is 38 and 6th term is 73...

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  10. Find 23rd term of the AP 7, 3, 1, -1, .... ,-3.

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  11. The 5th and 13th term of an A.P are 5 and -3 respectively. Find the A....

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  12. If the sum of the first 14 terms of an AP is 1050 and its first term i...

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  13. The next term of the G.P. x ,x^2+2,a n dx^3+10 is (729)/(16) b. 6 c. 0...

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  14. If x^2+9y^2+25 z^2=x y z((15)/x+5/y+3/z), then x ,y ,a n dz are in a...

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  15. If the sum of n terms of an A.P. is given by Sn=a+b n+c n^2, w h e r ...

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  16. Find the sum of 20th term of the A.P (x+y), (x-y), (x-3y), ....

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  17. Find the sum of the series 2+5+8+11+.....+191

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  18. If p ,q ,a n dr are inA.P., show that the pth, qth, and rth terms of a...

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  19. If n >1 , the value of the positive integer m for which n^m+1 divides ...

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  20. For an increasing A.P. a1, a2, an ifa1+a3+a5=-12 and a1a3a5=80 , then...

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