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Arithmetic Progression Worksheet for Olympiad

Maths Olympiad topic 29: Sequences and AP · Set 982 · 40 questions
TalentJR

How to solve it (Same step every time): In an AP the gap (common difference d) is always the same. nth term = a + (n − 1) × d, where a is the first term. Sum of n terms = n × (first + last) ÷ 2; so 1 + 2 + … + n = n × (n + 1) ÷ 2, and the first n odd numbers add up to n × n.

NameDateTime takenScore ___ / 40
  1. 1.What is the sum of all the whole numbers from 1 to 48? (a) 1152 (b) 1176 (c) 2352 (d) 1128
  2. 2.What is the 30th term of the AP 3, 6, 9, 12, …? (a) 93 (b) 90 (c) 87 (d) 91
  3. 3.What is the 12th term of the AP 20, 25, 30, 35, …? (a) 75 (b) 55 (c) 80 (d) 60
  4. 4.What is the sum of all the whole numbers from 1 to 80? (a) 3160 (b) 6480 (c) 3200 (d) 3240
  5. 5.What is the missing term in the AP 9, 12, 15, ?, 21? (a) 18 (b) 17 (c) 19 (d) 21
  6. 6.What is the 15th term of the AP 1, 3, 5, 7, …? (a) 31 (b) 29 (c) 28 (d) 30
  7. 7.What is the sum of the first 6 terms of the AP 8, 9, 10, …? (a) 66 (b) 13 (c) 126 (d) 63
  8. 8.What is the sum of the first 30 odd numbers (1 + 3 + 5 + …)? (a) 930 (b) 59 (c) 900 (d) 465
  9. 9.What is the sum of the first 10 terms of the AP 1, 3, 5, …? (a) 19 (b) 110 (c) 200 (d) 100
  10. 10.What is the 36th term of the AP 11, 15, 19, 23, …? (a) 155 (b) 140 (c) 151 (d) 144
  11. 11.What is the sum of all the whole numbers from 1 to 66? (a) 4422 (b) 2211 (c) 2145 (d) 2178
  12. 12.What is the sum of the first 11 terms of the AP 4, 5, 6, …? (a) 100 (b) 14 (c) 99 (d) 198
  13. 13.What is the missing term in the AP 5, 14, 23, ?, 41? (a) 33 (b) 41 (c) 32 (d) 31
  14. 14.What is the sum of the first 5 terms of the AP 5, 6, 7, …? (a) 36 (b) 70 (c) 9 (d) 35
  15. 15.What is the sum of the first 6 terms of the AP 4, 6, 8, …? (a) 60 (b) 14 (c) 54 (d) 108
  16. 16.What is the 35th term of the AP 13, 19, 25, 31, …? (a) 217 (b) 204 (c) 223 (d) 210
  17. 17.What is the 33rd term of the AP 16, 18, 20, 22, …? (a) 66 (b) 82 (c) 80 (d) 64
  18. 18.What is the missing term in the AP 15, 22, ?, 36, 43? (a) 36 (b) 30 (c) 29 (d) 28
  19. 19.What is the sum of the first 6 terms of the AP 1, 4, 7, …? (a) 60 (b) 51 (c) 16 (d) 102
  20. 20.What is the 20th term of the AP 5, 14, 23, 32, …? (a) 171 (b) 176 (c) 185 (d) 180
  21. 21.What is the sum of the first 26 odd numbers (1 + 3 + 5 + …)? (a) 702 (b) 676 (c) 51 (d) 351
  22. 22.What is the sum of all the whole numbers from 1 to 85? (a) 3570 (b) 3656 (c) 7310 (d) 3655
  23. 23.What is the 18th term of the AP 20, 26, 32, 38, …? (a) 102 (b) 128 (c) 108 (d) 122
  24. 24.What is the sum of the first 12 terms of the AP 8, 14, 20, …? (a) 74 (b) 984 (c) 528 (d) 492
  25. 25.What is the sum of the first 12 terms of the AP 6, 11, 16, …? (a) 432 (b) 402 (c) 804 (d) 61
  26. 26.What is the 21st term of the AP 15, 24, 33, 42, …? (a) 180 (b) 204 (c) 189 (d) 195
  27. 27.What is the 10th term of the AP 11, 19, 27, 35, …? (a) 80 (b) 91 (c) 83 (d) 72
  28. 28.What is the sum of the first 5 terms of the AP 1, 3, 5, …? (a) 25 (b) 50 (c) 9 (d) 30
  29. 29.What is the sum of the first 7 terms of the AP 9, 13, 17, …? (a) 33 (b) 147 (c) 294 (d) 161
  30. 30.What is the 35th term of the AP 16, 21, 26, 31, …? (a) 186 (b) 191 (c) 170 (d) 175
  31. 31.What is the 16th term of the AP 20, 23, 26, 29, …? (a) 45 (b) 65 (c) 48 (d) 68
  32. 32.What is the sum of the first 10 terms of the AP 9, 10, 11, …? (a) 135 (b) 140 (c) 270 (d) 18
  33. 33.What is the sum of all the whole numbers from 1 to 10? (a) 45 (b) 50 (c) 55 (d) 110
  34. 34.What is the sum of the first 21 odd numbers (1 + 3 + 5 + …)? (a) 231 (b) 41 (c) 441 (d) 462
  35. 35.What is the 19th term of the AP 4, 10, 16, 22, …? (a) 108 (b) 114 (c) 118 (d) 112
  36. 36.What is the sum of all the whole numbers from 1 to 59? (a) 3540 (b) 1771 (c) 1711 (d) 1770
  37. 37.What is the sum of all the whole numbers from 1 to 50? (a) 2550 (b) 1275 (c) 1250 (d) 1225
  38. 38.What is the sum of the first 6 terms of the AP 5, 9, 13, …? (a) 25 (b) 90 (c) 102 (d) 180
  39. 39.Which term of the AP 11, 17, 23, 29, … is 197? (a) 31st (b) 33rd (c) 34th (d) 32nd
  40. 40.Which term of the AP 13, 20, 27, 34, … is 97? (a) 12th (b) 15th (c) 14th (d) 13th

Answer key

  1. 1176
  2. 90
  3. 75
  4. 3240
  5. 18
  6. 29
  7. 63
  8. 900
  9. 100
  10. 151
  11. 2211
  12. 99
  13. 32
  14. 35
  15. 54
  16. 217
  17. 80
  18. 29
  19. 51
  20. 176
  21. 676
  22. 3655
  23. 122
  24. 492
  25. 402
  26. 195
  27. 83
  28. 25
  29. 147
  30. 186
  31. 65
  32. 135
  33. 55
  34. 441
  35. 112
  36. 1770
  37. 1275
  38. 90
  39. 32nd
  40. 13th

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