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Arithmetic Progression Worksheet for Olympiad

Maths Olympiad topic 29: Sequences and AP · Set 58 · 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 33rd term of the AP 14, 23, 32, 41, …? (a) 297 (b) 302 (c) 311 (d) 288
  2. 2.What is the missing term in the AP 10, ?, 16, 19, 22? (a) 13 (b) 14 (c) 16 (d) 12
  3. 3.What is the 18th term of the AP 6, 14, 22, 30, …? (a) 144 (b) 142 (c) 150 (d) 136
  4. 4.What is the 10th term of the AP 1, 10, 19, 28, …? (a) 82 (b) 91 (c) 90 (d) 81
  5. 5.What is the sum of the first 11 terms of the AP 8, 14, 20, …? (a) 418 (b) 68 (c) 451 (d) 836
  6. 6.What is the sum of the first 9 terms of the AP 9, 15, 21, …? (a) 594 (b) 324 (c) 297 (d) 57
  7. 7.What is the sum of the first 10 terms of the AP 3, 4, 5, …? (a) 150 (b) 80 (c) 12 (d) 75
  8. 8.What is the missing term in the AP 3, 5, 7, ?, 11? (a) 8 (b) 9 (c) 11 (d) 10
  9. 9.What is the missing term in the AP 12, ?, 18, 21, 24? (a) 14 (b) 15 (c) 18 (d) 16
  10. 10.What is the 32nd term of the AP 15, 22, 29, 36, …? (a) 217 (b) 239 (c) 224 (d) 232
  11. 11.What is the 14th term of the AP 19, 24, 29, 34, …? (a) 65 (b) 84 (c) 70 (d) 89
  12. 12.Which term of the AP 3, 8, 13, 18, … is 73? (a) 16th (b) 14th (c) 15th (d) 17th
  13. 13.What is the 15th term of the AP 19, 27, 35, 43, …? (a) 120 (b) 112 (c) 139 (d) 131
  14. 14.What is the sum of the first 12 terms of the AP 3, 7, 11, …? (a) 600 (b) 47 (c) 324 (d) 300
  15. 15.What is the sum of the first 6 terms of the AP 10, 12, 14, …? (a) 96 (b) 20 (c) 180 (d) 90
  16. 16.What is the sum of all the whole numbers from 1 to 69? (a) 2415 (b) 2416 (c) 4830 (d) 2346
  17. 17.What is the sum of the first 6 terms of the AP 9, 15, 21, …? (a) 144 (b) 288 (c) 162 (d) 39
  18. 18.What is the missing term in the AP 4, ?, 18, 25, 32? (a) 18 (b) 12 (c) 11 (d) 10
  19. 19.What is the sum of the first 30 odd numbers (1 + 3 + 5 + …)? (a) 465 (b) 900 (c) 59 (d) 930
  20. 20.What is the sum of the first 10 terms of the AP 4, 7, 10, …? (a) 350 (b) 190 (c) 175 (d) 31
  21. 21.Which term of the AP 4, 8, 12, 16, … is 128? (a) 31st (b) 34th (c) 32nd (d) 33rd
  22. 22.What is the sum of all the whole numbers from 1 to 80? (a) 3160 (b) 3200 (c) 6480 (d) 3240
  23. 23.What is the sum of the first 7 terms of the AP 9, 11, 13, …? (a) 105 (b) 21 (c) 210 (d) 112
  24. 24.What is the sum of the first 9 terms of the AP 2, 6, 10, …? (a) 34 (b) 162 (c) 180 (d) 324
  25. 25.What is the sum of all the whole numbers from 1 to 84? (a) 3528 (b) 7140 (c) 3570 (d) 3486
  26. 26.What is the 34th term of the AP 6, 10, 14, 18, …? (a) 138 (b) 132 (c) 142 (d) 136
  27. 27.What is the sum of the first 10 terms of the AP 6, 9, 12, …? (a) 390 (b) 33 (c) 195 (d) 210
  28. 28.What is the sum of the first 7 odd numbers (1 + 3 + 5 + …)? (a) 49 (b) 28 (c) 56 (d) 13
  29. 29.What is the sum of the first 18 odd numbers (1 + 3 + 5 + …)? (a) 324 (b) 342 (c) 35 (d) 171
  30. 30.Which term of the AP 2, 6, 10, 14, … is 38? (a) 10th (b) 11th (c) 9th (d) 12th
  31. 31.What is the 10th term of the AP 20, 22, 24, 26, …? (a) 40 (b) 20 (c) 38 (d) 18
  32. 32.What is the sum of all the whole numbers from 1 to 39? (a) 741 (b) 1560 (c) 781 (d) 780
  33. 33.What is the sum of all the whole numbers from 1 to 70? (a) 2415 (b) 4970 (c) 2485 (d) 2450
  34. 34.What is the 35th term of the AP 13, 17, 21, 25, …? (a) 140 (b) 136 (c) 153 (d) 149
  35. 35.Which term of the AP 18, 26, 34, 42, … is 138? (a) 15th (b) 17th (c) 18th (d) 16th
  36. 36.What is the 29th term of the AP 14, 19, 24, 29, …? (a) 145 (b) 159 (c) 154 (d) 140
  37. 37.What is the sum of the first 10 terms of the AP 6, 11, 16, …? (a) 310 (b) 285 (c) 51 (d) 570
  38. 38.What is the 29th term of the AP 11, 15, 19, 23, …? (a) 123 (b) 116 (c) 127 (d) 112
  39. 39.Which term of the AP 12, 15, 18, 21, … is 120? (a) 36th (b) 37th (c) 38th (d) 40th
  40. 40.Which term of the AP 4, 10, 16, 22, … is 58? (a) 11th (b) 9th (c) 12th (d) 10th

Answer key

  1. 302
  2. 13
  3. 142
  4. 82
  5. 418
  6. 297
  7. 75
  8. 9
  9. 15
  10. 232
  11. 84
  12. 15th
  13. 131
  14. 300
  15. 90
  16. 2415
  17. 144
  18. 11
  19. 900
  20. 175
  21. 32nd
  22. 3240
  23. 105
  24. 162
  25. 3570
  26. 138
  27. 195
  28. 49
  29. 324
  30. 10th
  31. 38
  32. 780
  33. 2485
  34. 149
  35. 16th
  36. 154
  37. 285
  38. 123
  39. 37th
  40. 10th

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