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Arithmetic Progression Worksheet for Olympiad

Maths Olympiad topic 29: Sequences and AP · Set 113 · 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 30 odd numbers (1 + 3 + 5 + …)? (a) 465 (b) 930 (c) 900 (d) 59
  2. 2.What is the 40th term of the AP 14, 22, 30, 38, …? (a) 334 (b) 326 (c) 312 (d) 320
  3. 3.What is the missing term in the AP 4, 12, ?, 28, 36? (a) 21 (b) 28 (c) 20 (d) 19
  4. 4.What is the missing term in the AP 6, ?, 22, 30, 38? (a) 13 (b) 22 (c) 15 (d) 14
  5. 5.What is the missing term in the AP 11, ?, 15, 17, 19? (a) 15 (b) 13 (c) 12 (d) 14
  6. 6.What is the 28th term of the AP 11, 13, 15, 17, …? (a) 56 (b) 65 (c) 54 (d) 67
  7. 7.Which term of the AP 1, 10, 19, 28, … is 154? (a) 19th (b) 18th (c) 20th (d) 17th
  8. 8.What is the sum of the first 28 odd numbers (1 + 3 + 5 + …)? (a) 406 (b) 812 (c) 784 (d) 55
  9. 9.What is the sum of the first 10 terms of the AP 2, 4, 6, …? (a) 120 (b) 110 (c) 220 (d) 20
  10. 10.What is the 33rd term of the AP 1, 4, 7, 10, …? (a) 100 (b) 96 (c) 99 (d) 97
  11. 11.What is the sum of the first 10 terms of the AP 10, 12, 14, …? (a) 380 (b) 190 (c) 200 (d) 28
  12. 12.What is the 18th term of the AP 20, 28, 36, 44, …? (a) 144 (b) 156 (c) 136 (d) 164
  13. 13.What is the sum of all the whole numbers from 1 to 12? (a) 72 (b) 156 (c) 66 (d) 78
  14. 14.Which term of the AP 1, 10, 19, 28, … is 307? (a) 34th (b) 37th (c) 36th (d) 35th
  15. 15.What is the missing term in the AP 18, 22, ?, 30, 34? (a) 27 (b) 25 (c) 30 (d) 26
  16. 16.What is the 14th term of the AP 16, 25, 34, 43, …? (a) 142 (b) 117 (c) 133 (d) 126
  17. 17.What is the sum of the first 10 terms of the AP 6, 11, 16, …? (a) 285 (b) 310 (c) 51 (d) 570
  18. 18.What is the 32nd term of the AP 9, 13, 17, 21, …? (a) 133 (b) 128 (c) 137 (d) 124
  19. 19.What is the 40th term of the AP 10, 19, 28, 37, …? (a) 361 (b) 351 (c) 360 (d) 370
  20. 20.Which term of the AP 1, 3, 5, 7, … is 17? (a) 11th (b) 10th (c) 8th (d) 9th
  21. 21.What is the sum of the first 12 terms of the AP 2, 7, 12, …? (a) 354 (b) 384 (c) 57 (d) 708
  22. 22.What is the 38th term of the AP 5, 9, 13, 17, …? (a) 157 (b) 152 (c) 148 (d) 153
  23. 23.What is the sum of the first 20 odd numbers (1 + 3 + 5 + …)? (a) 39 (b) 400 (c) 210 (d) 420
  24. 24.What is the sum of the first 10 terms of the AP 2, 8, 14, …? (a) 580 (b) 320 (c) 56 (d) 290
  25. 25.What is the 22nd term of the AP 14, 16, 18, 20, …? (a) 58 (b) 42 (c) 44 (d) 56
  26. 26.What is the sum of the first 9 terms of the AP 9, 10, 11, …? (a) 117 (b) 234 (c) 118 (d) 17
  27. 27.What is the sum of all the whole numbers from 1 to 83? (a) 3403 (b) 3487 (c) 6972 (d) 3486
  28. 28.What is the sum of the first 9 terms of the AP 10, 16, 22, …? (a) 306 (b) 333 (c) 58 (d) 612
  29. 29.What is the missing term in the AP 18, 21, 24, ?, 30? (a) 26 (b) 30 (c) 27 (d) 28
  30. 30.What is the missing term in the AP 12, 18, 24, ?, 36? (a) 29 (b) 31 (c) 36 (d) 30
  31. 31.Which term of the AP 11, 13, 15, 17, … is 61? (a) 25th (b) 27th (c) 26th (d) 28th
  32. 32.What is the sum of the first 26 odd numbers (1 + 3 + 5 + …)? (a) 702 (b) 51 (c) 676 (d) 351
  33. 33.What is the sum of all the whole numbers from 1 to 46? (a) 1081 (b) 1058 (c) 1035 (d) 2162
  34. 34.What is the sum of the first 8 terms of the AP 10, 12, 14, …? (a) 272 (b) 24 (c) 144 (d) 136
  35. 35.What is the sum of the first 12 terms of the AP 5, 6, 7, …? (a) 126 (b) 132 (c) 16 (d) 252
  36. 36.What is the 34th term of the AP 5, 10, 15, 20, …? (a) 171 (b) 175 (c) 170 (d) 165
  37. 37.What is the 16th term of the AP 1, 8, 15, 22, …? (a) 112 (b) 113 (c) 105 (d) 106
  38. 38.What is the missing term in the AP 7, ?, 21, 28, 35? (a) 21 (b) 13 (c) 15 (d) 14
  39. 39.What is the sum of the first 6 terms of the AP 4, 10, 16, …? (a) 114 (b) 34 (c) 132 (d) 228
  40. 40.What is the sum of the first 11 terms of the AP 3, 9, 15, …? (a) 726 (b) 396 (c) 63 (d) 363

Answer key

  1. 900
  2. 326
  3. 20
  4. 14
  5. 13
  6. 65
  7. 18th
  8. 784
  9. 110
  10. 97
  11. 190
  12. 156
  13. 78
  14. 35th
  15. 26
  16. 133
  17. 285
  18. 133
  19. 361
  20. 9th
  21. 354
  22. 153
  23. 400
  24. 290
  25. 56
  26. 117
  27. 3486
  28. 306
  29. 27
  30. 30
  31. 26th
  32. 676
  33. 1081
  34. 136
  35. 126
  36. 170
  37. 106
  38. 14
  39. 114
  40. 363

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