questionrEarly access

Sequences and Series

Showing 50 of 519 · 519 total
  1. 351.Let x,y,z be positive real numbers such that x+y+z=12 and x^3y^4z^5=(0.1)(600)^3.
  2. 352.If the sum of the first ten terms of the series (135)^2+(225)^2+(315)^2+4^2+(445)^2+ is 16…
  3. 353.For xR, x-1, if (1+x)^2016+x(1+x)^2015+x^2(1+x)^2014++x^2016=_i=0^2016a_ix^i, then a_17 is…
  4. 354.If m is the A.M.
  5. 355.The sum of the 3rd and the 4th terms of a G.P.
  6. 356.The sum of the first 9 terms of the series whose n-th term is T_n=(1+2++nn)^2 is:
  7. 357.If _n=1^5(1)/(n(n+1)(n+2)(n+3))=(k)/(3), then k is equal to:
  8. 358.The value of _r=16^30(r+2)(r-3) is equal to:
  9. 359.Let and be the roots of the equation px^2+qx+r=0, p0.
  10. 360.The sum of the first 20 terms common between the series 3+7+11+15+ and 1+6+11+16+ is:
  11. 361.Given an A.P.
  12. 362.Three positive numbers form an increasing G.P.
  13. 363.The least positive integer n such that 1-23-23^2--23^n-1<1100, is:
  14. 364.In a geometric progression, if the ratio of the sum of the first 5 terms to the sum of the…
  15. 365.The coefficient of x^50 in the binomial expansion of (1+x)^1000+x(1+x)^999+x^2(1+x)^998++x…
  16. 366.Let G be the geometric mean of two positive numbers a and b, and M be the arithmetic mean …
  17. 367.If (10)^9+2(11)(10)^8+3(11)^2(10)^7++10(11)^9=k(10)^9, then k is equal to:
  18. 368.The number of terms in an A.P.
  19. 369.If the sum 13+15+1^2+2^2 --- precisely, 1+11^2+11^2+2^2+ up to 20 terms, using the general…
  20. 370.Let a_1,a_2,a_3, be an A.P.
  21. 371.The sum of the series 1+11+2+11+2+3+ up to 10 terms, is:
  22. 372.If a_1,a_2,a_3,,a_n, are in A.P.
  23. 373.Given the sum of the first n terms of an A.P.
  24. 374.Given a sequence of 4 numbers, the first three of which are in G.P.
  25. 375.The sum of the first 20 terms of the sequence 0.7, 0.77, 0.777, is:
  26. 376.The value of 1^2+3^2+5^2++25^2 is:
  27. 377.The sum of the series 12^2+24^2+36^2+ up to 10 terms is:
  28. 378.The sum 31^2+51^2+2^2+71^2+2^2+3^2+ up to 11 terms is:
  29. 379.The sum of the series 1^2+22^2+3^2+24^2+5^2+26^2++2(2m)^2 is:
  30. 380.The difference between the fourth term and the first term of a Geometric Progression is 52…
  31. 381.If a,b,c,d and p are distinct real numbers such that (a^2+b^2+c^2)p^2-2p(ab+bc+cd)+(b^2+c^…
  32. 382.The sum of the series 11+√2+1√2+√3+1√3+√4+ up to 15 terms is:
  33. 383.Suppose and (0) are such that (+), , (-) are in A.P.
  34. 384.The sum of the series 1+43+109+2827+ up to n terms is:
  35. 385.If the A.M.
  36. 386.If 100 times the 100th term of an A.P.
  37. 387.Statement-1: The sum of the series 1+(1+2+4)+(4+6+9)+(9+12+16)++(361+380+400) is 8000.
  38. 388.Let a_n be the n-th term of an A.P.
  39. 389.If the sum of the series 1^2+22^2+3^2+24^2+5^2+26^2+ up to n terms, when n is even, is n(n…
  40. 390.A man saves 200 in each of the first three months of his service.
  41. 391.A person is to count 4500 currency notes.
  42. 392.The sum to infinite terms of the series 1+23+63^2+103^3+143^4+ is:
  43. 393.The first two terms of a geometric progression add up to 12.
  44. 394.In a geometric progression consisting of positive terms, each term equals the sum of the n…
  45. 395.The sum of the series 12!-13!+14!- up to infinity is:
  46. 396.Let a_1,a_2,a_3, be terms of an A.P.
  47. 397.The value of _k=1^10[(2k)/(11)+i(2k)/(11)] is:
  48. 398.If the expansion in powers of x of the function 1(1-ax)(1-bx) is a_0+a_1x+a_2x^2+a_3x^3+, …
  49. 399.If a_1,a_2,,a_n are in H.P., then the expression a_1a_2+a_2a_3++a_n-1a_n is equal to:
  50. 400.If the coefficients of the r-th, (r+1)-th, and (r+2)-th terms in the binomial expansion of…