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Arithmetic Progression Worksheet for Olympiad

Maths Olympiad topic 29: Sequences and AP · Set 633 · 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 the first 12 terms of the AP 3, 5, 7, …? (a) 25 (b) 168 (c) 180 (d) 336
  2. 2.What is the missing term in the AP 5, 7, ?, 11, 13? (a) 8 (b) 10 (c) 9 (d) 11
  3. 3.What is the missing term in the AP 10, 13, ?, 19, 22? (a) 16 (b) 19 (c) 17 (d) 15
  4. 4.Which term of the AP 3, 9, 15, 21, … is 111? (a) 20th (b) 21st (c) 19th (d) 18th
  5. 5.What is the sum of all the whole numbers from 1 to 45? (a) 990 (b) 1036 (c) 2070 (d) 1035
  6. 6.What is the 31st term of the AP 8, 12, 16, 20, …? (a) 128 (b) 120 (c) 124 (d) 132
  7. 7.What is the missing term in the AP 15, 21, 27, ?, 39? (a) 39 (b) 34 (c) 33 (d) 32
  8. 8.Which term of the AP 17, 20, 23, 26, … is 122? (a) 35th (b) 38th (c) 37th (d) 36th
  9. 9.What is the missing term in the AP 12, 16, ?, 24, 28? (a) 24 (b) 19 (c) 20 (d) 21
  10. 10.What is the sum of the first 16 odd numbers (1 + 3 + 5 + …)? (a) 256 (b) 272 (c) 31 (d) 136
  11. 11.What is the missing term in the AP 9, ?, 27, 36, 45? (a) 27 (b) 19 (c) 18 (d) 17
  12. 12.What is the sum of the first 5 terms of the AP 4, 9, 14, …? (a) 24 (b) 140 (c) 75 (d) 70
  13. 13.What is the sum of the first 10 terms of the AP 8, 11, 14, …? (a) 35 (b) 215 (c) 430 (d) 230
  14. 14.What is the sum of the first 5 terms of the AP 3, 5, 7, …? (a) 11 (b) 70 (c) 40 (d) 35
  15. 15.What is the 30th term of the AP 18, 21, 24, 27, …? (a) 105 (b) 87 (c) 90 (d) 108
  16. 16.Which term of the AP 18, 27, 36, 45, … is 234? (a) 27th (b) 24th (c) 26th (d) 25th
  17. 17.What is the 11th term of the AP 8, 13, 18, 23, …? (a) 58 (b) 55 (c) 50 (d) 63
  18. 18.What is the sum of the first 20 odd numbers (1 + 3 + 5 + …)? (a) 400 (b) 210 (c) 39 (d) 420
  19. 19.What is the sum of the first 12 terms of the AP 10, 12, 14, …? (a) 252 (b) 264 (c) 32 (d) 504
  20. 20.What is the 36th term of the AP 8, 15, 22, 29, …? (a) 252 (b) 253 (c) 260 (d) 245
  21. 21.What is the 14th term of the AP 5, 10, 15, 20, …? (a) 70 (b) 75 (c) 71 (d) 65
  22. 22.Which term of the AP 11, 18, 25, 32, … is 116? (a) 18th (b) 17th (c) 15th (d) 16th
  23. 23.What is the sum of the first 5 terms of the AP 9, 13, 17, …? (a) 170 (b) 25 (c) 85 (d) 95
  24. 24.Which term of the AP 11, 19, 27, 35, … is 155? (a) 21st (b) 20th (c) 18th (d) 19th
  25. 25.What is the sum of all the whole numbers from 1 to 66? (a) 2145 (b) 2211 (c) 4422 (d) 2178
  26. 26.What is the sum of all the whole numbers from 1 to 26? (a) 351 (b) 325 (c) 702 (d) 338
  27. 27.What is the sum of all the whole numbers from 1 to 71? (a) 2485 (b) 2557 (c) 2556 (d) 5112
  28. 28.What is the 22nd term of the AP 14, 21, 28, 35, …? (a) 154 (b) 168 (c) 161 (d) 147
  29. 29.Which term of the AP 12, 16, 20, 24, … is 72? (a) 18th (b) 15th (c) 16th (d) 17th
  30. 30.What is the sum of all the whole numbers from 1 to 95? (a) 4465 (b) 4561 (c) 9120 (d) 4560
  31. 31.What is the 14th term of the AP 2, 5, 8, 11, …? (a) 42 (b) 44 (c) 39 (d) 41
  32. 32.What is the sum of the first 7 terms of the AP 3, 4, 5, …? (a) 43 (b) 9 (c) 84 (d) 42
  33. 33.What is the 28th term of the AP 1, 4, 7, 10, …? (a) 84 (b) 85 (c) 82 (d) 81
  34. 34.What is the sum of the first 22 odd numbers (1 + 3 + 5 + …)? (a) 253 (b) 43 (c) 506 (d) 484
  35. 35.What is the 11th term of the AP 4, 7, 10, 13, …? (a) 33 (b) 37 (c) 30 (d) 34
  36. 36.What is the sum of the first 5 terms of the AP 1, 3, 5, …? (a) 9 (b) 30 (c) 50 (d) 25
  37. 37.What is the sum of the first 6 terms of the AP 1, 6, 11, …? (a) 162 (b) 26 (c) 96 (d) 81
  38. 38.What is the 24th term of the AP 4, 13, 22, 31, …? (a) 207 (b) 211 (c) 220 (d) 216
  39. 39.What is the sum of all the whole numbers from 1 to 67? (a) 2278 (b) 2279 (c) 4556 (d) 2211
  40. 40.What is the missing term in the AP 2, 8, 14, ?, 26? (a) 19 (b) 21 (c) 26 (d) 20

Answer key

  1. 168
  2. 9
  3. 16
  4. 19th
  5. 1035
  6. 128
  7. 33
  8. 36th
  9. 20
  10. 256
  11. 18
  12. 70
  13. 215
  14. 35
  15. 105
  16. 25th
  17. 58
  18. 400
  19. 252
  20. 253
  21. 70
  22. 16th
  23. 85
  24. 19th
  25. 2211
  26. 351
  27. 2556
  28. 161
  29. 16th
  30. 4560
  31. 41
  32. 42
  33. 82
  34. 484
  35. 34
  36. 25
  37. 81
  38. 211
  39. 2278
  40. 20

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