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Let `a _(1), a_(2), a_(3),…….., a_(n)` be real numbers in arithmatic progressin such that `a _(1) =15 and a_(2)` is an integer.Given ` sum _( r=1) ^(10) (a_(r)) ^(2) =1185. If S_(n) = sum _(r =1) ^(n) a_(r) and ` maximum value of n is N for which `S_(n) ge S_((n +1)), ` then find `N -10.`

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VIKAS GUPTA (BLACK BOOK)-SEQUENCE AND SERIES -EXERCISE (SUBJECTIVE TYPE PROBLEMS)
  1. The sum of all digits of n for which sum (r =1) ^(n ) r 2 ^(r ) = 2+2^...

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  2. If lim ( x to oo) (r +2)/(2 ^(r+1) r (r+1))=1/k, then k =

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  3. The value of sum (r =1) ^(oo) (8r)/(4r ^(4) +1) is equal to :

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  4. Three non-zero real numbers from an A.P. and the squares of these numb...

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  5. The sum of the fourth and twelfth term of an arithmetic progression is...

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  6. In an increasing sequence of four positive integers, the first 3 terms...

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  7. The limit of (1)/(n ^(4)) sum (k =1) ^(n) k (k +2) (k +4) as n to oo i...

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  8. Which is the last digit of 1+2+3+……+ n if the last digit of 1 ^(3) + ...

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  9. There distinct positive numbers, a,b,c are in G.P. while log (c) a, lo...

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  10. The numbers 1/3, 1/3 log (x) y, 1/3 log (y) z, 1/7 log (x) x are in H...

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  11. If sum ( k =1) ^(oo) (k^(2))/(3 ^(k))=p/q, where p and q are relativel...

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  12. The sum of the terms of an infinitely decreassing Geometric Progressio...

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  13. A cricketer has to score 4500 runs. Let a (n) denotes the number of ru...

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  14. If x=10 sum(r=3) ^(100) (1)/((r ^(2) -4)), then [x]= (where [.] deno...

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  15. Let f (n)=(4n + sqrt(4n ^(2) +1))/( sqrt(2n +1 )+sqrt(2n-1)),n in N th...

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  16. Find the sum of series 1+1/2+1/3+1/4+1/6+1/8+1/9+1/12+…… oo, where the...

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  17. Let a (1), a(2), a(3),…….., a(n) be real numbers in arithmatic progres...

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  18. Let the roots of the equation 24 x ^(3) -14x ^(2) + kx +3=0 form a geo...

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  19. How many ordered pair (s) satisfy log (x ^(2) + (1)/(3) y ^(3) + (1)/(...

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  20. The value of xyz is 55 or 343/55 according as the sequence a,x,y,z,b i...

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