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Arithmetic Progression Worksheet for Olympiad

Maths Olympiad topic 29: Sequences and AP · Set 342 · 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 13th term of the AP 4, 6, 8, 10, …? (a) 30 (b) 28 (c) 26 (d) 24
  2. 2.What is the sum of all the whole numbers from 1 to 28? (a) 392 (b) 378 (c) 406 (d) 812
  3. 3.What is the sum of the first 18 odd numbers (1 + 3 + 5 + …)? (a) 342 (b) 324 (c) 35 (d) 171
  4. 4.What is the 20th term of the AP 15, 21, 27, 33, …? (a) 120 (b) 114 (c) 129 (d) 135
  5. 5.What is the 12th term of the AP 6, 15, 24, 33, …? (a) 114 (b) 99 (c) 108 (d) 105
  6. 6.What is the sum of the first 7 terms of the AP 10, 11, 12, …? (a) 92 (b) 91 (c) 182 (d) 16
  7. 7.What is the missing term in the AP 12, 18, 24, ?, 36? (a) 30 (b) 36 (c) 31 (d) 29
  8. 8.What is the 11th term of the AP 13, 17, 21, 25, …? (a) 53 (b) 57 (c) 44 (d) 40
  9. 9.What is the 39th term of the AP 11, 13, 15, 17, …? (a) 76 (b) 78 (c) 87 (d) 89
  10. 10.What is the sum of the first 9 terms of the AP 5, 7, 9, …? (a) 117 (b) 126 (c) 234 (d) 21
  11. 11.What is the sum of the first 12 odd numbers (1 + 3 + 5 + …)? (a) 156 (b) 23 (c) 144 (d) 78
  12. 12.What is the missing term in the AP 6, ?, 24, 33, 42? (a) 16 (b) 14 (c) 15 (d) 24
  13. 13.What is the 37th term of the AP 4, 6, 8, 10, …? (a) 78 (b) 74 (c) 76 (d) 72
  14. 14.What is the missing term in the AP 3, 7, ?, 15, 19? (a) 10 (b) 11 (c) 15 (d) 12
  15. 15.What is the sum of all the whole numbers from 1 to 19? (a) 171 (b) 380 (c) 191 (d) 190
  16. 16.What is the 15th term of the AP 5, 11, 17, 23, …? (a) 90 (b) 95 (c) 89 (d) 84
  17. 17.What is the sum of the first 11 terms of the AP 8, 13, 18, …? (a) 368 (b) 363 (c) 58 (d) 726
  18. 18.What is the sum of the first 11 terms of the AP 1, 7, 13, …? (a) 682 (b) 341 (c) 374 (d) 61
  19. 19.What is the missing term in the AP 7, ?, 15, 19, 23? (a) 15 (b) 10 (c) 11 (d) 12
  20. 20.What is the sum of the first 5 terms of the AP 5, 7, 9, …? (a) 90 (b) 45 (c) 13 (d) 50
  21. 21.What is the 36th term of the AP 11, 15, 19, 23, …? (a) 155 (b) 140 (c) 144 (d) 151
  22. 22.What is the 28th term of the AP 20, 29, 38, 47, …? (a) 263 (b) 272 (c) 252 (d) 243
  23. 23.What is the missing term in the AP 17, 21, ?, 29, 33? (a) 25 (b) 24 (c) 29 (d) 26
  24. 24.What is the sum of all the whole numbers from 1 to 73? (a) 2628 (b) 5402 (c) 2702 (d) 2701
  25. 25.What is the sum of all the whole numbers from 1 to 13? (a) 78 (b) 182 (c) 92 (d) 91
  26. 26.What is the sum of the first 6 terms of the AP 10, 13, 16, …? (a) 114 (b) 210 (c) 105 (d) 25
  27. 27.What is the sum of the first 6 terms of the AP 9, 14, 19, …? (a) 144 (b) 129 (c) 258 (d) 34
  28. 28.Which term of the AP 7, 11, 15, 19, … is 55? (a) 15th (b) 12th (c) 14th (d) 13th
  29. 29.What is the sum of the first 12 terms of the AP 7, 12, 17, …? (a) 414 (b) 62 (c) 828 (d) 444
  30. 30.What is the sum of all the whole numbers from 1 to 67? (a) 2211 (b) 2279 (c) 2278 (d) 4556
  31. 31.What is the sum of all the whole numbers from 1 to 77? (a) 6006 (b) 3003 (c) 3004 (d) 2926
  32. 32.What is the sum of the first 6 terms of the AP 8, 12, 16, …? (a) 120 (b) 216 (c) 28 (d) 108
  33. 33.What is the missing term in the AP 19, ?, 37, 46, 55? (a) 29 (b) 27 (c) 28 (d) 37
  34. 34.What is the sum of the first 5 terms of the AP 2, 4, 6, …? (a) 10 (b) 60 (c) 35 (d) 30
  35. 35.What is the missing term in the AP 2, ?, 18, 26, 34? (a) 10 (b) 11 (c) 9 (d) 18
  36. 36.What is the missing term in the AP 11, 19, ?, 35, 43? (a) 27 (b) 26 (c) 28 (d) 35
  37. 37.What is the sum of the first 11 odd numbers (1 + 3 + 5 + …)? (a) 66 (b) 121 (c) 21 (d) 132
  38. 38.What is the missing term in the AP 6, 9, 12, ?, 18? (a) 15 (b) 18 (c) 16 (d) 14
  39. 39.What is the sum of the first 8 terms of the AP 8, 11, 14, …? (a) 160 (b) 148 (c) 29 (d) 296
  40. 40.What is the 15th term of the AP 2, 5, 8, 11, …? (a) 45 (b) 42 (c) 44 (d) 47

Answer key

  1. 28
  2. 406
  3. 324
  4. 129
  5. 105
  6. 91
  7. 30
  8. 53
  9. 87
  10. 117
  11. 144
  12. 15
  13. 76
  14. 11
  15. 190
  16. 89
  17. 363
  18. 341
  19. 11
  20. 45
  21. 151
  22. 263
  23. 25
  24. 2701
  25. 91
  26. 105
  27. 129
  28. 13th
  29. 414
  30. 2278
  31. 3003
  32. 108
  33. 28
  34. 30
  35. 10
  36. 27
  37. 121
  38. 15
  39. 148
  40. 44

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