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Sequences and Series

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  1. 1.Let =3+4+8+9+13+14+ upto 40 terms.
  2. 2.Consider the quadratic equation (n^2-2n+2)x^2-3x+(n^2-2n+2)^2=0,n R.
  3. 3.The sum 1+(1)/(2)(1^2+2^2)+(1)/(3)(1^2+2^2+3^2)+ upto 10 terms is equal to :
  4. 4.The value of 1^3-2^3+3^3-+15^3 is:
  5. 5.The sum of the first ten terms of an A.P.
  6. 6.Let , be the roots of the equation x^2-x+p=0 and , be the roots the equation x^2-4x+q=0; p…
  7. 7.If the sum of the first 10 terms of the series (1)/(1+1^4 4)+(2)/(1+2^4 4)+(3)/(1+3^4 4)+(…
  8. 8.Let A_1,A_2,A_3, ..,A_39 be 39 arithmetic means between the numbers 59 and 159.
  9. 9.Let the sum of the first n terms of an A.P.
  10. 10._10^n=1((528)/(n(n+1)(n+2))) is equal to:
  11. 11.The first term of an A.P.
  12. 12.Let a_1, a_2, a_3, be an A.P.
  13. 13.The sum (1^3)/(1) + (1^3 + 2^3)/(1 + 3) + (1^3 + 2^3 + 3^3)/(1 + 3 + 5) + up to 8 terms, i…
  14. 14.Let the arithmetic mean of (1)/(a) and (1)/(b) be (5)/(16), a>2.
  15. 15.63^26 + 10 13^25 + 10 23^24 + 10 2^23^23 + + 10 2^243 is equal to :
  16. 16.The common difference of the A.P.: a_1,a_2, ,a_m is 13 more than the common difference of …
  17. 17.Let a_1, a_2, a_3, a_4 be an A.P.
  18. 18.((1)/(3)+(4)/(7))+(13^2+(1)/(3) (4)/(7)+4^27^2)+(13^3+13^2 (4)/(7)+(1)/(3) 4^27^2+4^37^3)+…
  19. 19.Let 729,81,9,1, be a sequence and P_n denote the product of the first n terms of this sequ…
  20. 20.Consider an A.P.: a_1,a_2, ,a_n;a_1>0.
  21. 21.Let _k=1^na_k= n^2+ n.
  22. 22.If the sum of the first four terms of an A.P.
  23. 23.The positive integer n, for which the solutions of the equation x(x+2) + (x+2)(x+4) + + (x…
  24. 24.Let a_1, (a_2)/(2), (a_3)/(2^2), , a_102^9 be a G.P.
  25. 25.Let a_1, a_2, a_3, be a G.P.
  26. 26.If 11^4+12^4+13^4+ = ^490, 11^4+13^4+15^4+ = , 12^4+14^4+16^4+ = , then ( )/( ) is equal t…
  27. 27.Let a_n be the n^th term of an A.P.
  28. 28.If the sum of the second, fourth and sixth terms of a G.P.
  29. 29.Let x_1, x_2, x_3, x_4 be in a geometric progression.
  30. 30.If the sum of the first 20 terms of the series (4 1)/(4+3 1^2+1^4)+(4 2)/(4+3 2^2+2^4)+(4 …
  31. 31.Consider two sets A and B, each containing three numbers in A.P.
  32. 32.Let A=1,6,11,16, and B=9,16,23,30, be the sets consisting of the first 2025 terms of two a…
  33. 33.1+3+5^2+7+9^2+ upto 40 terms is equal to
  34. 34.The sum 1+(1+3)/(2!)+(1+3+5)/(3!)+(1+3+5+7)/(4!)+ upto terms, is equal to
  35. 35.Let a_1, a_2, a_3, .
  36. 36.The sum 1+3+11+25+45+71+ upto 20 terms, is equal to
  37. 37.The number of terms of an A.P.
  38. 38.Let a_1,a_2,a_3, be in an A.P.
  39. 39.Consider an A.
  40. 40.For positive integers n, if 4a_n=(n^2+5n+6) and S_n= _k=1^n(1a_k), then the value of 507S_…
  41. 41.Let a_n be a sequence such that a_0=0,a_1=(1)/(2) and 2a_n+2=5a_n+1-3a_n,n=0,1,2,3,.
  42. 42.Let T_r be the r^ term of an A.P.
  43. 43.In an arithmetic progression, if S_40=1030 and S_12=57, then S_30-S_10 is equal to :
  44. 44.If 7=5+(1)/(7)(5+ )+17^2(5+2 )+17^3(5+3 )+ , then the value of is :
  45. 45.Let S_n=(1)/(2)+(1)/(6)+(1)/(12)+(1)/(20)+ upto n terms.
  46. 46.If the first term of an A.P.
  47. 47.Suppose that the number of terms in an A.P.
  48. 48.Let a_1, a_2, a_3, be a G.P.
  49. 49.Let a,ar,ar^2, ............
  50. 50.If the sum of the series (1)/(1 (1+d))+(1)/((1+d)(1+2d))+ +(1)/((1+9d)(1+10d)) is equal to…