questionrEarly access

Sequences and Series

Showing 50 of 519 · 519 total
  1. 151.Consider an A.P.
  2. 152.The number of terms of an A.P.
  3. 153.The sum 1 + 1+32! + 1+3+53! + 1+3+5+74! + is equal to:
  4. 154.1^2+3+5^2+7+9^2+11+ up to 40 terms is equal to:
  5. 155.Consider two sets A and B, each containing three numbers in A.P.
  6. 156.If the sum of the first 20 terms of the series _r (4r)/(4+3r^2+r^4) is mn, where m,n are c…
  7. 157.Let x_1,x_2,x_3,x_4 be in a geometric progression.
  8. 158.Let a_n denote the nth term of an A.P.
  9. 159.It is given that _n=1^(1)/(n^4) = (^4)/(90).
  10. 160.The 20th term from the end of a given progression is:
  11. 161.If in a G.P.
  12. 162.In an A.P., the sixth term a_6=2.
  13. 163.If _e a, _e b, _e c are in A.P., and _e a - _e 2b, _e 2b - _e 3c, _e 3c - _e a are also in…
  14. 164.If each term of a geometric progression a_1,a_2,a_3, with a_1=18 and a_2 a_1 is the arithm…
  15. 165.Let = 1^2+4^2+8^2+13^2+19^2+26^2+ up to 10 terms, and let be a related quantity defined in…
  16. 166.Let a and b be two distinct positive real numbers.
  17. 167.Let the 2nd, 8th and 44th terms of a non-constant A.P.
  18. 168.For three positive integers p,q,r, suppose x^pq^2=y^qr=z^p^2r and r=pq+1, such that 3, 3_y…
  19. 169.The 4th term of a G.P.
  20. 170.If 1^3+2^3+3^3+ up to n terms13+25+37+ up to n terms = 95, then the value of n is ________…
  21. 171.Let A_1, A_2, A_3 be three A.P.s with the same common difference d, having first terms A, …
  22. 172.For two positive numbers a, b, if a, b, 118 are in a geometric progression, while 1a, 10, …
  23. 173.Let a_1,a_2,a_3, be a G.P.
  24. 174.Let a_k and b_k, kN, be two G.P.s with common ratios r_1 and r_2 respectively, such that a…
  25. 175.Let a_1=b_1=1, and for n2: a_n = a_n-1+(n-1), b_n = b_n-1+a_n-1.
  26. 176.If a_n = -24n^2-16n+15, then a_1+a_2++a_25 is equal to:
  27. 177.The parabolas ax^2+2bx+cy=0 and dx^2+2ex+fy=0 intersect on the line y=1.
  28. 178.The 8th common term of the series S_1 = 3+7+11+15+19+ and S_2 = 1+6+11+16+21+ is ________.
  29. 179.Let y=f(x) represent a parabola with focus (-12, 0) and directrix y=-12.
  30. 180.Let a_1,a_2,,a_n be in A.P.
  31. 181.Let a_1,a_2,a_3, be an A.P.
  32. 182.The sum 11^2 - 23^2 + 35^2 - 47^2 + 59^2 - + 1529^2 is ________.
  33. 183.The sum to 10 terms of the series 11+1^2+1^4+21+2^2+2^4+31+3^2+3^4+ is:
  34. 184.Let a_1=8, a_2, a_3, , a_n be an A.P.
  35. 185.The number of 3-digit numbers that are divisible by either 2 or 3 but not divisible by 7 i…
  36. 186.The sum of the common terms of the three arithmetic progressions 3,7,11,15,,399; 2,5,8,11,…
  37. 187.Let S_k = 1+2++kk and _j=1^nS_j^2 = nA(Bn^2+Cn+D), where A,B,C,DN and A has the least poss…
  38. 188.Let 0<z<y<x be three real numbers such that 1x, 1y, 1z are in an arithmetic progression, a…
  39. 189.If f(x) = (1^)x+_e123x_e1234-1^, x>0, then the least value of f(f(x))+f!(f!(4x)) is:
  40. 190.Suppose a_1, a_2, 2, a_3, a_4 be in an arithmetico-geometric progression (with the middle …
  41. 191.Let S = 109 + 1085+1075^2++25^107+15^108.
  42. 192.Let a,b,c,d be positive real numbers such that a+b+c+d=11.
  43. 193.For kN, if the sum of the series 1+4k+8k^2+13k^3+19k^4+ is 10, then the value of k is ____…
  44. 194.Let a_n be a sequence such that a_1+a_2++a_n = n^2+3n(n+1)(n+2).
  45. 195.Let s_1,s_2,,s_10 respectively be the sums to 12 terms of 10 A.P.s whose first terms are 1…
  46. 196.Let a_1,a_2,a_3, be a G.P.
  47. 197.Let A_1 and A_2 be two arithmetic means, and G_1,G_2,G_3 be three geometric means, of two …
  48. 198.If the sum of the series [12-13+(1)/(2^2)-(1)/(23)+(1)/(3^2)+(1)/(2^3)-(1)/(2^23)+(1)/(23^…
  49. 199.If a_i_i=1^n, where n is an even integer, is an arithmetic progression with common differe…
  50. 200.The greatest integer less than or equal to the sum of the first 100 terms of the sequence …