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Arithmetic Progression Worksheet for Olympiad

Maths Olympiad topic 29: Sequences and AP · Set 442 · 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 12 terms of the AP 4, 9, 14, …? (a) 408 (b) 378 (c) 59 (d) 756
  2. 2.Which term of the AP 10, 19, 28, 37, … is 91? (a) 12th (b) 10th (c) 11th (d) 9th
  3. 3.What is the sum of all the whole numbers from 1 to 21? (a) 232 (b) 210 (c) 231 (d) 462
  4. 4.What is the sum of the first 30 odd numbers (1 + 3 + 5 + …)? (a) 465 (b) 930 (c) 900 (d) 59
  5. 5.What is the 17th term of the AP 8, 16, 24, 32, …? (a) 144 (b) 136 (c) 137 (d) 128
  6. 6.What is the 35th term of the AP 1, 5, 9, 13, …? (a) 136 (b) 141 (c) 137 (d) 140
  7. 7.What is the 20th term of the AP 9, 13, 17, 21, …? (a) 85 (b) 76 (c) 80 (d) 89
  8. 8.What is the missing term in the AP 15, ?, 33, 42, 51? (a) 25 (b) 33 (c) 23 (d) 24
  9. 9.Which term of the AP 3, 7, 11, 15, … is 39? (a) 12th (b) 10th (c) 9th (d) 11th
  10. 10.What is the sum of the first 10 terms of the AP 4, 8, 12, …? (a) 40 (b) 440 (c) 220 (d) 240
  11. 11.What is the sum of the first 12 terms of the AP 9, 13, 17, …? (a) 744 (b) 53 (c) 396 (d) 372
  12. 12.What is the sum of the first 5 terms of the AP 2, 6, 10, …? (a) 60 (b) 100 (c) 50 (d) 18
  13. 13.Which term of the AP 6, 13, 20, 27, … is 62? (a) 10th (b) 8th (c) 9th (d) 11th
  14. 14.What is the 29th term of the AP 7, 15, 23, 31, …? (a) 231 (b) 239 (c) 232 (d) 224
  15. 15.What is the sum of all the whole numbers from 1 to 11? (a) 132 (b) 66 (c) 67 (d) 55
  16. 16.What is the 16th term of the AP 17, 21, 25, 29, …? (a) 77 (b) 81 (c) 60 (d) 64
  17. 17.What is the 33rd term of the AP 2, 9, 16, 23, …? (a) 231 (b) 226 (c) 233 (d) 224
  18. 18.What is the 24th term of the AP 7, 13, 19, 25, …? (a) 151 (b) 138 (c) 144 (d) 145
  19. 19.What is the sum of the first 6 terms of the AP 1, 7, 13, …? (a) 96 (b) 31 (c) 192 (d) 114
  20. 20.What is the sum of all the whole numbers from 1 to 77? (a) 6006 (b) 3004 (c) 3003 (d) 2926
  21. 21.What is the sum of the first 6 terms of the AP 2, 3, 4, …? (a) 30 (b) 54 (c) 27 (d) 7
  22. 22.Which term of the AP 7, 13, 19, 25, … is 181? (a) 31st (b) 32nd (c) 29th (d) 30th
  23. 23.What is the sum of the first 11 terms of the AP 2, 6, 10, …? (a) 42 (b) 264 (c) 242 (d) 484
  24. 24.What is the sum of the first 10 odd numbers (1 + 3 + 5 + …)? (a) 110 (b) 19 (c) 100 (d) 55
  25. 25.What is the sum of the first 9 terms of the AP 5, 9, 13, …? (a) 189 (b) 37 (c) 207 (d) 378
  26. 26.What is the sum of the first 18 odd numbers (1 + 3 + 5 + …)? (a) 342 (b) 171 (c) 35 (d) 324
  27. 27.What is the sum of the first 29 odd numbers (1 + 3 + 5 + …)? (a) 435 (b) 57 (c) 870 (d) 841
  28. 28.Which term of the AP 15, 24, 33, 42, … is 312? (a) 35th (b) 36th (c) 34th (d) 33rd
  29. 29.What is the sum of all the whole numbers from 1 to 91? (a) 4186 (b) 4095 (c) 8372 (d) 4187
  30. 30.What is the 12th term of the AP 15, 24, 33, 42, …? (a) 123 (b) 114 (c) 108 (d) 99
  31. 31.What is the sum of the first 22 odd numbers (1 + 3 + 5 + …)? (a) 506 (b) 43 (c) 484 (d) 253
  32. 32.What is the missing term in the AP 18, 21, 24, ?, 30? (a) 28 (b) 30 (c) 27 (d) 26
  33. 33.Which term of the AP 14, 19, 24, 29, … is 54? (a) 8th (b) 10th (c) 11th (d) 9th
  34. 34.What is the sum of the first 7 odd numbers (1 + 3 + 5 + …)? (a) 28 (b) 49 (c) 13 (d) 56
  35. 35.What is the missing term in the AP 19, 28, 37, ?, 55? (a) 47 (b) 45 (c) 55 (d) 46
  36. 36.What is the missing term in the AP 19, ?, 23, 25, 27? (a) 20 (b) 22 (c) 23 (d) 21
  37. 37.What is the missing term in the AP 3, ?, 15, 21, 27? (a) 8 (b) 15 (c) 9 (d) 10
  38. 38.What is the sum of the first 6 terms of the AP 9, 14, 19, …? (a) 144 (b) 129 (c) 34 (d) 258
  39. 39.What is the 23rd term of the AP 14, 22, 30, 38, …? (a) 190 (b) 198 (c) 184 (d) 176
  40. 40.What is the sum of the first 9 terms of the AP 5, 11, 17, …? (a) 261 (b) 522 (c) 288 (d) 53

Answer key

  1. 378
  2. 10th
  3. 231
  4. 900
  5. 136
  6. 137
  7. 85
  8. 24
  9. 10th
  10. 220
  11. 372
  12. 50
  13. 9th
  14. 231
  15. 66
  16. 77
  17. 226
  18. 145
  19. 96
  20. 3003
  21. 27
  22. 30th
  23. 242
  24. 100
  25. 189
  26. 324
  27. 841
  28. 34th
  29. 4186
  30. 114
  31. 484
  32. 27
  33. 9th
  34. 49
  35. 46
  36. 21
  37. 9
  38. 129
  39. 190
  40. 261

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