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Arithmetic Progression Worksheet for Olympiad

Maths Olympiad topic 29: Sequences and AP · Set 400 · 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.Which term of the AP 16, 19, 22, 25, … is 94? (a) 28th (b) 26th (c) 29th (d) 27th
  2. 2.What is the sum of the first 12 terms of the AP 1, 3, 5, …? (a) 144 (b) 288 (c) 156 (d) 23
  3. 3.What is the missing term in the AP 9, 13, ?, 21, 25? (a) 17 (b) 18 (c) 16 (d) 21
  4. 4.Which term of the AP 11, 15, 19, 23, … is 119? (a) 29th (b) 27th (c) 30th (d) 28th
  5. 5.What is the 17th term of the AP 18, 27, 36, 45, …? (a) 162 (b) 171 (c) 144 (d) 153
  6. 6.Which term of the AP 8, 16, 24, 32, … is 272? (a) 36th (b) 34th (c) 33rd (d) 35th
  7. 7.What is the 35th term of the AP 6, 10, 14, 18, …? (a) 140 (b) 146 (c) 142 (d) 136
  8. 8.What is the 22nd term of the AP 1, 6, 11, 16, …? (a) 105 (b) 110 (c) 111 (d) 106
  9. 9.What is the sum of all the whole numbers from 1 to 19? (a) 380 (b) 190 (c) 171 (d) 191
  10. 10.Which term of the AP 5, 14, 23, 32, … is 230? (a) 26th (b) 25th (c) 27th (d) 28th
  11. 11.What is the 37th term of the AP 3, 11, 19, 27, …? (a) 288 (b) 296 (c) 291 (d) 299
  12. 12.What is the sum of the first 8 odd numbers (1 + 3 + 5 + …)? (a) 72 (b) 64 (c) 36 (d) 15
  13. 13.What is the sum of the first 7 odd numbers (1 + 3 + 5 + …)? (a) 49 (b) 13 (c) 28 (d) 56
  14. 14.What is the 23rd term of the AP 3, 8, 13, 18, …? (a) 110 (b) 115 (c) 118 (d) 113
  15. 15.What is the sum of the first 9 odd numbers (1 + 3 + 5 + …)? (a) 81 (b) 45 (c) 17 (d) 90
  16. 16.What is the 15th term of the AP 10, 17, 24, 31, …? (a) 115 (b) 98 (c) 105 (d) 108
  17. 17.What is the sum of all the whole numbers from 1 to 46? (a) 2162 (b) 1035 (c) 1058 (d) 1081
  18. 18.What is the missing term in the AP 8, ?, 26, 35, 44? (a) 26 (b) 18 (c) 16 (d) 17
  19. 19.What is the sum of all the whole numbers from 1 to 27? (a) 379 (b) 378 (c) 351 (d) 756
  20. 20.Which term of the AP 11, 13, 15, 17, … is 31? (a) 13th (b) 12th (c) 10th (d) 11th
  21. 21.What is the missing term in the AP 18, 25, 32, ?, 46? (a) 39 (b) 46 (c) 40 (d) 38
  22. 22.Which term of the AP 6, 11, 16, 21, … is 41? (a) 10th (b) 7th (c) 8th (d) 9th
  23. 23.What is the sum of the first 10 terms of the AP 9, 10, 11, …? (a) 140 (b) 18 (c) 270 (d) 135
  24. 24.What is the 30th term of the AP 19, 26, 33, 40, …? (a) 203 (b) 229 (c) 210 (d) 222
  25. 25.What is the 36th term of the AP 19, 26, 33, 40, …? (a) 264 (b) 245 (c) 252 (d) 271
  26. 26.What is the sum of the first 11 terms of the AP 8, 14, 20, …? (a) 68 (b) 418 (c) 836 (d) 451
  27. 27.What is the sum of the first 9 terms of the AP 3, 7, 11, …? (a) 189 (b) 342 (c) 171 (d) 35
  28. 28.What is the sum of the first 7 terms of the AP 10, 16, 22, …? (a) 196 (b) 46 (c) 217 (d) 392
  29. 29.What is the sum of the first 9 terms of the AP 5, 9, 13, …? (a) 189 (b) 37 (c) 207 (d) 378
  30. 30.What is the 13th term of the AP 1, 9, 17, 25, …? (a) 97 (b) 105 (c) 96 (d) 104
  31. 31.What is the sum of all the whole numbers from 1 to 52? (a) 1326 (b) 1378 (c) 2756 (d) 1352
  32. 32.Which term of the AP 10, 19, 28, 37, … is 181? (a) 21st (b) 20th (c) 19th (d) 22nd
  33. 33.What is the missing term in the AP 12, 16, ?, 24, 28? (a) 20 (b) 21 (c) 24 (d) 19
  34. 34.What is the 18th term of the AP 5, 14, 23, 32, …? (a) 153 (b) 162 (c) 167 (d) 158
  35. 35.What is the sum of the first 10 terms of the AP 9, 12, 15, …? (a) 450 (b) 240 (c) 36 (d) 225
  36. 36.What is the 37th term of the AP 7, 13, 19, 25, …? (a) 222 (b) 229 (c) 223 (d) 216
  37. 37.What is the sum of all the whole numbers from 1 to 18? (a) 153 (b) 162 (c) 171 (d) 342
  38. 38.What is the 16th term of the AP 14, 22, 30, 38, …? (a) 142 (b) 128 (c) 120 (d) 134
  39. 39.What is the sum of the first 11 terms of the AP 1, 7, 13, …? (a) 341 (b) 61 (c) 682 (d) 374
  40. 40.What is the sum of the first 7 terms of the AP 1, 6, 11, …? (a) 112 (b) 224 (c) 31 (d) 117

Answer key

  1. 27th
  2. 144
  3. 17
  4. 28th
  5. 162
  6. 34th
  7. 142
  8. 106
  9. 190
  10. 26th
  11. 291
  12. 64
  13. 49
  14. 113
  15. 81
  16. 108
  17. 1081
  18. 17
  19. 378
  20. 11th
  21. 39
  22. 8th
  23. 135
  24. 222
  25. 264
  26. 418
  27. 171
  28. 196
  29. 189
  30. 97
  31. 1378
  32. 20th
  33. 20
  34. 158
  35. 225
  36. 223
  37. 171
  38. 134
  39. 341
  40. 112

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