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Arithmetic Progression Worksheet for Olympiad

Maths Olympiad topic 29: Sequences and AP · Set 546 · 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 missing term in the AP 13, ?, 23, 28, 33? (a) 17 (b) 18 (c) 19 (d) 23
  2. 2.What is the missing term in the AP 2, 10, 18, ?, 34? (a) 34 (b) 25 (c) 27 (d) 26
  3. 3.What is the missing term in the AP 12, 18, ?, 30, 36? (a) 30 (b) 25 (c) 23 (d) 24
  4. 4.What is the sum of the first 10 terms of the AP 8, 12, 16, …? (a) 44 (b) 260 (c) 280 (d) 520
  5. 5.What is the 17th term of the AP 9, 13, 17, 21, …? (a) 64 (b) 68 (c) 73 (d) 77
  6. 6.What is the sum of all the whole numbers from 1 to 78? (a) 6162 (b) 3081 (c) 3042 (d) 3003
  7. 7.What is the missing term in the AP 10, 18, 26, ?, 42? (a) 33 (b) 34 (c) 35 (d) 42
  8. 8.Which term of the AP 12, 17, 22, 27, … is 82? (a) 17th (b) 16th (c) 14th (d) 15th
  9. 9.What is the sum of the first 5 terms of the AP 10, 12, 14, …? (a) 18 (b) 140 (c) 70 (d) 75
  10. 10.Which term of the AP 1, 4, 7, 10, … is 79? (a) 29th (b) 26th (c) 28th (d) 27th
  11. 11.What is the 14th term of the AP 14, 17, 20, 23, …? (a) 39 (b) 56 (c) 42 (d) 53
  12. 12.What is the 28th term of the AP 15, 22, 29, 36, …? (a) 196 (b) 189 (c) 204 (d) 211
  13. 13.What is the 13th term of the AP 1, 6, 11, 16, …? (a) 61 (b) 60 (c) 65 (d) 66
  14. 14.What is the 25th term of the AP 12, 19, 26, 33, …? (a) 187 (b) 168 (c) 175 (d) 180
  15. 15.What is the missing term in the AP 16, ?, 24, 28, 32? (a) 19 (b) 21 (c) 24 (d) 20
  16. 16.What is the sum of the first 9 odd numbers (1 + 3 + 5 + …)? (a) 45 (b) 17 (c) 90 (d) 81
  17. 17.What is the sum of the first 6 terms of the AP 2, 6, 10, …? (a) 84 (b) 144 (c) 72 (d) 22
  18. 18.What is the sum of the first 12 terms of the AP 3, 4, 5, …? (a) 108 (b) 102 (c) 204 (d) 14
  19. 19.What is the sum of the first 12 terms of the AP 3, 6, 9, …? (a) 468 (b) 234 (c) 36 (d) 252
  20. 20.What is the sum of all the whole numbers from 1 to 88? (a) 3872 (b) 7832 (c) 3828 (d) 3916
  21. 21.What is the 10th term of the AP 17, 19, 21, 23, …? (a) 18 (b) 20 (c) 37 (d) 35
  22. 22.What is the missing term in the AP 4, 9, ?, 19, 24? (a) 14 (b) 19 (c) 15 (d) 13
  23. 23.What is the 16th term of the AP 16, 25, 34, 43, …? (a) 144 (b) 135 (c) 151 (d) 160
  24. 24.What is the sum of the first 6 terms of the AP 9, 10, 11, …? (a) 14 (b) 72 (c) 138 (d) 69
  25. 25.What is the sum of the first 9 terms of the AP 3, 4, 5, …? (a) 63 (b) 64 (c) 126 (d) 11
  26. 26.Which term of the AP 2, 10, 18, 26, … is 74? (a) 12th (b) 11th (c) 10th (d) 9th
  27. 27.What is the sum of the first 5 terms of the AP 9, 10, 11, …? (a) 55 (b) 13 (c) 56 (d) 110
  28. 28.What is the sum of the first 5 terms of the AP 8, 13, 18, …? (a) 180 (b) 90 (c) 95 (d) 28
  29. 29.Which term of the AP 16, 20, 24, 28, … is 80? (a) 18th (b) 20th (c) 17th (d) 16th
  30. 30.What is the sum of the first 9 terms of the AP 2, 3, 4, …? (a) 55 (b) 10 (c) 108 (d) 54
  31. 31.Which term of the AP 2, 4, 6, 8, … is 60? (a) 32nd (b) 31st (c) 29th (d) 30th
  32. 32.What is the sum of the first 9 terms of the AP 6, 10, 14, …? (a) 38 (b) 216 (c) 396 (d) 198
  33. 33.What is the sum of the first 16 odd numbers (1 + 3 + 5 + …)? (a) 272 (b) 136 (c) 256 (d) 31
  34. 34.What is the sum of the first 30 odd numbers (1 + 3 + 5 + …)? (a) 59 (b) 900 (c) 465 (d) 930
  35. 35.What is the 32nd term of the AP 13, 22, 31, 40, …? (a) 301 (b) 288 (c) 292 (d) 279
  36. 36.What is the sum of all the whole numbers from 1 to 91? (a) 8372 (b) 4186 (c) 4095 (d) 4187
  37. 37.What is the 34th term of the AP 6, 12, 18, 24, …? (a) 210 (b) 205 (c) 198 (d) 204
  38. 38.What is the sum of all the whole numbers from 1 to 25? (a) 650 (b) 326 (c) 325 (d) 300
  39. 39.What is the sum of the first 8 odd numbers (1 + 3 + 5 + …)? (a) 72 (b) 15 (c) 64 (d) 36
  40. 40.What is the 30th term of the AP 11, 13, 15, 17, …? (a) 71 (b) 58 (c) 60 (d) 69

Answer key

  1. 18
  2. 26
  3. 24
  4. 260
  5. 73
  6. 3081
  7. 34
  8. 15th
  9. 70
  10. 27th
  11. 53
  12. 204
  13. 61
  14. 180
  15. 20
  16. 81
  17. 72
  18. 102
  19. 234
  20. 3916
  21. 35
  22. 14
  23. 151
  24. 69
  25. 63
  26. 10th
  27. 55
  28. 90
  29. 17th
  30. 54
  31. 30th
  32. 198
  33. 256
  34. 900
  35. 292
  36. 4186
  37. 204
  38. 325
  39. 64
  40. 69

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