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Sequences and Series

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  1. 301.Let f:RR satisfy f(x+y)=f(x)+f(y), x,yR.
  2. 302.Let a,b,c be the 7th, 11th and 13th terms respectively of a non-constant A.P.
  3. 303.If a,b,c are three distinct real numbers in G.P.
  4. 304.The sum of the series 1+6+9(1^2+2^2+3^2)7+12(1^2+2^2+3^2+4^2)9+15(1^2+2^2++5^2)11+ up to 1…
  5. 305.The sum of all values of (0,2) satisfying ^22+^42=34 is:
  6. 306.Let , be the roots of x^2 - x(+1)+=0 (0<<45^), <.
  7. 307.Let a_1,a_2,,a_10 be a G.P.
  8. 308.The sum of an infinite geometric series with positive terms is 3, and the sum of the cubes…
  9. 309.Let S_n = 1+q+q^2++q^n and T_n = 1+q+12+(q+12)^2++(q+12)^n, where q is a real number, q1.
  10. 310.The product of three consecutive terms of a G.P.
  11. 311.Let S_k = 1+2+3++kk.
  12. 312.If the sum of the first 15 terms of the series 34^3+112^3+214^3+3^3+334^3+ is equal to 225…
  13. 313.If ^nC_4, ^nC_5, ^nC_6 are in A.P., then n can be:
  14. 314.If the 19th term of a nonzero A.P.
  15. 315.The sum of all two-digit positive numbers which, when divided by 7, yield 2 or 5 as remain…
  16. 316.Let a_1,a_2,,a_30 be an A.P., S=_i=1^30a_i and T=_i=1^15a_(2i-1).
  17. 317.If three distinct numbers a,b,c are in G.P., and the equations ax^2+2bx+c=0 and dx^2+2ex+f…
  18. 318.For xR, let [x] denote the greatest integer x.
  19. 319.The sum 31^31^2+5(1^3+2^3)1^2+2^2+7(1^3+2^3+3^3)1^2+2^2+3^2+ up to the 10th term is:
  20. 320.The sum [1+(1^3+2^3)/(1+2)+(1^3+2^3+3^3)/(1+2+3)++(1^3+2^3++15^3)/(1+2++15) - 12(1+2++15)]…
  21. 321.The sum of the series 1+23+35+47+ up to the 11th term is:
  22. 322.Some identical balls are arranged in rows to form an equilateral triangle: the first row h…
  23. 323.The sum _k=1^20k2^k is equal to:
  24. 324.Let S_n denote the sum of the first n terms of an A.P.
  25. 325.If a_1,a_2,a_3, are in A.P.
  26. 326.If a_1,a_2,,a_n are in A.P.
  27. 327.Let the sum of the first n terms of a non-constant A.P.
  28. 328.Let _k=1^10f(a+k) = 16(2^10-1), where the function f satisfies f(x+y)=f(x)f(y) for all nat…
  29. 329.If the sum and product of the first three terms in an A.P.
  30. 330.The sum of all natural numbers n such that 100<n<200 and (91,n)>1 is:
  31. 331.If ,, are three consecutive terms of a non-constant G.P.
  32. 332.Let a,b,c be in G.P.
  33. 333.Let 1x_1,1x_2,1x_3, (x_i0) be in A.P.
  34. 334.If x_1,x_2,,x_n and 1h_1,1h_2,,1h_n are two A.P.'s such that x_3=h_2=8 and x_8=h_7=20, the…
  35. 335.If b is the first term of an infinite G.P.
  36. 336.Let A_n = 34-34^2+34^3-+(-1)^n-134^n and B_n=1-A_n.
  37. 337.If a,b,c are in A.P.
  38. 338.The sum of the first 20 terms of the series 1+32+74+158+3116+ is:
  39. 339.Let A be the sum of the first 20 terms and B be the sum of the first 40 terms of the serie…
  40. 340.Let a_1,a_2,a_3,,a_49 be in A.P.
  41. 341.For any three positive real numbers a,b,c: 9(25a^2+b^2)+25(c^2-3ac)=15b(3a+c).
  42. 342.If three positive numbers a,b,c are in A.P.
  43. 343.If the arithmetic mean of two numbers a and b, a>b>0, is five times their geometric mean, …
  44. 344.Let a,b,cR.
  45. 345.Let S_n=11^3+1+21^3+2^3+1+2+31^3+2^3+3^3++1+2++n1^3+2^3++n^3.
  46. 346.If the sum of the first n terms of the series √3+√75+√243+√507+ is 435√3, then n equals:
  47. 347.Let a_1,a_2,a_3,,a_n be in A.P.
  48. 348.If the 2nd, 5th and 9th terms of a non-constant A.P.
  49. 349.Let z=1+ai be a complex number, a>0, such that z^3 is a real number.
  50. 350.If A>0,B>0 and A+B=6, then the minimum value of A+ B is: