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Arithmetic Progression Worksheet for Olympiad

Maths Olympiad topic 29: Sequences and AP · Set 279 · 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 70? (a) 2450 (b) 4970 (c) 2415 (d) 2485
  2. 2.What is the 18th term of the AP 12, 17, 22, 27, …? (a) 90 (b) 97 (c) 102 (d) 85
  3. 3.What is the 19th term of the AP 17, 24, 31, 38, …? (a) 150 (b) 126 (c) 143 (d) 133
  4. 4.What is the 35th term of the AP 6, 8, 10, 12, …? (a) 68 (b) 70 (c) 74 (d) 76
  5. 5.What is the 13th term of the AP 6, 8, 10, 12, …? (a) 24 (b) 32 (c) 30 (d) 26
  6. 6.What is the 39th term of the AP 14, 17, 20, 23, …? (a) 128 (b) 114 (c) 131 (d) 117
  7. 7.What is the sum of the first 8 odd numbers (1 + 3 + 5 + …)? (a) 72 (b) 64 (c) 36 (d) 15
  8. 8.What is the 35th term of the AP 5, 9, 13, 17, …? (a) 140 (b) 141 (c) 145 (d) 136
  9. 9.What is the 36th term of the AP 12, 16, 20, 24, …? (a) 144 (b) 140 (c) 152 (d) 156
  10. 10.What is the sum of the first 9 terms of the AP 9, 13, 17, …? (a) 450 (b) 243 (c) 41 (d) 225
  11. 11.What is the 15th term of the AP 2, 11, 20, 29, …? (a) 137 (b) 126 (c) 135 (d) 128
  12. 12.What is the missing term in the AP 11, 15, ?, 23, 27? (a) 20 (b) 18 (c) 23 (d) 19
  13. 13.What is the sum of the first 12 terms of the AP 10, 13, 16, …? (a) 636 (b) 318 (c) 336 (d) 43
  14. 14.What is the sum of the first 10 odd numbers (1 + 3 + 5 + …)? (a) 100 (b) 110 (c) 55 (d) 19
  15. 15.What is the missing term in the AP 8, 13, ?, 23, 28? (a) 23 (b) 17 (c) 18 (d) 19
  16. 16.What is the sum of the first 7 terms of the AP 1, 7, 13, …? (a) 154 (b) 133 (c) 37 (d) 266
  17. 17.Which term of the AP 5, 8, 11, 14, … is 113? (a) 38th (b) 36th (c) 39th (d) 37th
  18. 18.What is the 33rd term of the AP 4, 7, 10, 13, …? (a) 99 (b) 103 (c) 96 (d) 100
  19. 19.What is the missing term in the AP 15, ?, 29, 36, 43? (a) 23 (b) 21 (c) 29 (d) 22
  20. 20.What is the sum of the first 7 terms of the AP 2, 7, 12, …? (a) 119 (b) 32 (c) 124 (d) 238
  21. 21.What is the 30th term of the AP 20, 28, 36, 44, …? (a) 240 (b) 232 (c) 260 (d) 252
  22. 22.What is the 11th term of the AP 8, 12, 16, 20, …? (a) 48 (b) 40 (c) 52 (d) 44
  23. 23.What is the 16th term of the AP 1, 5, 9, 13, …? (a) 65 (b) 60 (c) 64 (d) 61
  24. 24.What is the sum of all the whole numbers from 1 to 62? (a) 1891 (b) 3906 (c) 1922 (d) 1953
  25. 25.What is the sum of the first 6 terms of the AP 3, 6, 9, …? (a) 72 (b) 18 (c) 63 (d) 126
  26. 26.What is the 15th term of the AP 4, 6, 8, 10, …? (a) 28 (b) 30 (c) 32 (d) 34
  27. 27.What is the sum of the first 12 terms of the AP 3, 6, 9, …? (a) 36 (b) 252 (c) 234 (d) 468
  28. 28.What is the missing term in the AP 9, ?, 23, 30, 37? (a) 16 (b) 15 (c) 23 (d) 17
  29. 29.Which term of the AP 2, 9, 16, 23, … is 268? (a) 40th (b) 41st (c) 39th (d) 38th
  30. 30.What is the sum of the first 6 terms of the AP 8, 12, 16, …? (a) 216 (b) 120 (c) 108 (d) 28
  31. 31.What is the missing term in the AP 14, 17, 20, ?, 26? (a) 24 (b) 23 (c) 26 (d) 22
  32. 32.What is the sum of the first 7 terms of the AP 2, 4, 6, …? (a) 112 (b) 63 (c) 56 (d) 14
  33. 33.Which term of the AP 3, 7, 11, 15, … is 47? (a) 11th (b) 12th (c) 14th (d) 13th
  34. 34.What is the 39th term of the AP 1, 9, 17, 25, …? (a) 305 (b) 304 (c) 313 (d) 312
  35. 35.Which term of the AP 15, 20, 25, 30, … is 205? (a) 40th (b) 38th (c) 41st (d) 39th
  36. 36.Which term of the AP 2, 10, 18, 26, … is 106? (a) 14th (b) 15th (c) 16th (d) 13th
  37. 37.What is the 21st term of the AP 11, 20, 29, 38, …? (a) 180 (b) 200 (c) 189 (d) 191
  38. 38.What is the 30th term of the AP 5, 7, 9, 11, …? (a) 60 (b) 58 (c) 63 (d) 65
  39. 39.What is the sum of the first 12 terms of the AP 3, 4, 5, …? (a) 102 (b) 204 (c) 108 (d) 14
  40. 40.What is the sum of the first 7 terms of the AP 6, 11, 16, …? (a) 147 (b) 294 (c) 36 (d) 152

Answer key

  1. 2485
  2. 97
  3. 143
  4. 74
  5. 30
  6. 128
  7. 64
  8. 141
  9. 152
  10. 225
  11. 128
  12. 19
  13. 318
  14. 100
  15. 18
  16. 133
  17. 37th
  18. 100
  19. 22
  20. 119
  21. 252
  22. 48
  23. 61
  24. 1953
  25. 63
  26. 32
  27. 234
  28. 16
  29. 39th
  30. 108
  31. 23
  32. 56
  33. 12th
  34. 305
  35. 39th
  36. 14th
  37. 191
  38. 63
  39. 102
  40. 147

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