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Arithmetic Progression Worksheet for Olympiad

Maths Olympiad topic 29: Sequences and AP · Set 438 · 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 36th term of the AP 3, 5, 7, 9, …? (a) 75 (b) 73 (c) 70 (d) 72
  2. 2.What is the sum of the first 9 terms of the AP 10, 16, 22, …? (a) 58 (b) 333 (c) 612 (d) 306
  3. 3.What is the missing term in the AP 2, ?, 6, 8, 10? (a) 5 (b) 3 (c) 6 (d) 4
  4. 4.What is the 16th term of the AP 20, 28, 36, 44, …? (a) 148 (b) 128 (c) 140 (d) 120
  5. 5.What is the sum of the first 14 odd numbers (1 + 3 + 5 + …)? (a) 210 (b) 196 (c) 105 (d) 27
  6. 6.What is the sum of all the whole numbers from 1 to 33? (a) 1122 (b) 528 (c) 562 (d) 561
  7. 7.Which term of the AP 14, 20, 26, 32, … is 62? (a) 11th (b) 9th (c) 8th (d) 10th
  8. 8.What is the missing term in the AP 6, ?, 16, 21, 26? (a) 12 (b) 16 (c) 11 (d) 10
  9. 9.What is the sum of all the whole numbers from 1 to 44? (a) 946 (b) 968 (c) 990 (d) 1980
  10. 10.What is the sum of the first 11 terms of the AP 3, 5, 7, …? (a) 143 (b) 286 (c) 154 (d) 23
  11. 11.What is the 13th term of the AP 16, 22, 28, 34, …? (a) 72 (b) 88 (c) 94 (d) 78
  12. 12.What is the 15th term of the AP 8, 14, 20, 26, …? (a) 90 (b) 98 (c) 84 (d) 92
  13. 13.What is the missing term in the AP 1, ?, 5, 7, 9? (a) 2 (b) 4 (c) 3 (d) 5
  14. 14.What is the sum of the first 9 terms of the AP 3, 8, 13, …? (a) 43 (b) 207 (c) 212 (d) 414
  15. 15.What is the 11th term of the AP 6, 13, 20, 27, …? (a) 77 (b) 83 (c) 76 (d) 70
  16. 16.What is the 14th term of the AP 5, 9, 13, 17, …? (a) 52 (b) 57 (c) 56 (d) 61
  17. 17.What is the sum of the first 8 odd numbers (1 + 3 + 5 + …)? (a) 36 (b) 72 (c) 15 (d) 64
  18. 18.What is the sum of the first 13 odd numbers (1 + 3 + 5 + …)? (a) 25 (b) 182 (c) 169 (d) 91
  19. 19.What is the sum of the first 6 terms of the AP 3, 4, 5, …? (a) 8 (b) 36 (c) 66 (d) 33
  20. 20.What is the sum of the first 12 odd numbers (1 + 3 + 5 + …)? (a) 156 (b) 78 (c) 23 (d) 144
  21. 21.What is the missing term in the AP 13, 19, 25, ?, 37? (a) 37 (b) 32 (c) 30 (d) 31
  22. 22.What is the sum of the first 5 terms of the AP 7, 11, 15, …? (a) 85 (b) 23 (c) 150 (d) 75
  23. 23.What is the 17th term of the AP 14, 16, 18, 20, …? (a) 34 (b) 48 (c) 32 (d) 46
  24. 24.What is the 13th term of the AP 19, 27, 35, 43, …? (a) 96 (b) 123 (c) 104 (d) 115
  25. 25.Which term of the AP 3, 12, 21, 30, … is 111? (a) 14th (b) 15th (c) 13th (d) 12th
  26. 26.What is the sum of all the whole numbers from 1 to 97? (a) 4656 (b) 9506 (c) 4754 (d) 4753
  27. 27.What is the sum of all the whole numbers from 1 to 18? (a) 153 (b) 342 (c) 162 (d) 171
  28. 28.What is the 39th term of the AP 17, 23, 29, 35, …? (a) 234 (b) 228 (c) 251 (d) 245
  29. 29.What is the missing term in the AP 18, ?, 28, 33, 38? (a) 22 (b) 24 (c) 23 (d) 28
  30. 30.What is the sum of the first 26 odd numbers (1 + 3 + 5 + …)? (a) 676 (b) 51 (c) 702 (d) 351
  31. 31.What is the missing term in the AP 20, 27, ?, 41, 48? (a) 41 (b) 35 (c) 34 (d) 33
  32. 32.What is the missing term in the AP 8, 13, ?, 23, 28? (a) 19 (b) 23 (c) 17 (d) 18
  33. 33.What is the 30th term of the AP 19, 27, 35, 43, …? (a) 232 (b) 240 (c) 251 (d) 259
  34. 34.Which term of the AP 11, 14, 17, 20, … is 59? (a) 19th (b) 18th (c) 17th (d) 16th
  35. 35.What is the sum of the first 12 terms of the AP 1, 5, 9, …? (a) 45 (b) 552 (c) 276 (d) 300
  36. 36.What is the 39th term of the AP 3, 8, 13, 18, …? (a) 198 (b) 195 (c) 193 (d) 190
  37. 37.What is the missing term in the AP 10, ?, 14, 16, 18? (a) 13 (b) 14 (c) 12 (d) 11
  38. 38.What is the sum of the first 6 terms of the AP 2, 7, 12, …? (a) 174 (b) 27 (c) 102 (d) 87
  39. 39.What is the sum of all the whole numbers from 1 to 20? (a) 190 (b) 200 (c) 420 (d) 210
  40. 40.What is the 31st term of the AP 16, 24, 32, 40, …? (a) 264 (b) 240 (c) 248 (d) 256

Answer key

  1. 73
  2. 306
  3. 4
  4. 140
  5. 196
  6. 561
  7. 9th
  8. 11
  9. 990
  10. 143
  11. 88
  12. 92
  13. 3
  14. 207
  15. 76
  16. 57
  17. 64
  18. 169
  19. 33
  20. 144
  21. 31
  22. 75
  23. 46
  24. 115
  25. 13th
  26. 4753
  27. 171
  28. 245
  29. 23
  30. 676
  31. 34
  32. 18
  33. 251
  34. 17th
  35. 276
  36. 193
  37. 12
  38. 87
  39. 210
  40. 256

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