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Arithmetic Progression Worksheet for Olympiad

Maths Olympiad topic 29: Sequences and AP · Set 555 · 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 all the whole numbers from 1 to 17? (a) 153 (b) 306 (c) 136 (d) 154
  2. 2.What is the sum of the first 9 terms of the AP 5, 6, 7, …? (a) 82 (b) 162 (c) 81 (d) 13
  3. 3.What is the missing term in the AP 20, 27, 34, ?, 48? (a) 42 (b) 41 (c) 48 (d) 40
  4. 4.What is the 21st term of the AP 10, 19, 28, 37, …? (a) 180 (b) 190 (c) 189 (d) 199
  5. 5.What is the sum of all the whole numbers from 1 to 52? (a) 1378 (b) 1326 (c) 2756 (d) 1352
  6. 6.What is the missing term in the AP 17, 23, 29, ?, 41? (a) 41 (b) 35 (c) 36 (d) 34
  7. 7.What is the sum of the first 6 terms of the AP 10, 12, 14, …? (a) 180 (b) 20 (c) 96 (d) 90
  8. 8.What is the 25th term of the AP 15, 24, 33, 42, …? (a) 240 (b) 231 (c) 216 (d) 225
  9. 9.What is the sum of the first 7 terms of the AP 10, 15, 20, …? (a) 180 (b) 40 (c) 350 (d) 175
  10. 10.Which term of the AP 2, 6, 10, 14, … is 38? (a) 12th (b) 9th (c) 11th (d) 10th
  11. 11.Which term of the AP 5, 14, 23, 32, … is 356? (a) 42nd (b) 41st (c) 40th (d) 39th
  12. 12.What is the 29th term of the AP 1, 5, 9, 13, …? (a) 116 (b) 117 (c) 113 (d) 112
  13. 13.What is the 25th term of the AP 18, 27, 36, 45, …? (a) 243 (b) 225 (c) 234 (d) 216
  14. 14.What is the sum of the first 10 terms of the AP 2, 4, 6, …? (a) 120 (b) 110 (c) 20 (d) 220
  15. 15.What is the 38th term of the AP 3, 6, 9, 12, …? (a) 114 (b) 115 (c) 111 (d) 117
  16. 16.What is the 28th term of the AP 14, 16, 18, 20, …? (a) 70 (b) 54 (c) 68 (d) 56
  17. 17.What is the 25th term of the AP 19, 23, 27, 31, …? (a) 100 (b) 96 (c) 119 (d) 115
  18. 18.What is the sum of the first 10 terms of the AP 2, 6, 10, …? (a) 400 (b) 220 (c) 200 (d) 38
  19. 19.What is the 38th term of the AP 20, 27, 34, 41, …? (a) 286 (b) 279 (c) 259 (d) 266
  20. 20.What is the sum of the first 21 odd numbers (1 + 3 + 5 + …)? (a) 441 (b) 231 (c) 462 (d) 41
  21. 21.What is the sum of the first 11 terms of the AP 1, 6, 11, …? (a) 291 (b) 286 (c) 51 (d) 572
  22. 22.What is the missing term in the AP 4, 11, 18, ?, 32? (a) 25 (b) 32 (c) 24 (d) 26
  23. 23.What is the 40th term of the AP 12, 16, 20, 24, …? (a) 172 (b) 168 (c) 156 (d) 160
  24. 24.Which term of the AP 18, 27, 36, 45, … is 144? (a) 14th (b) 16th (c) 17th (d) 15th
  25. 25.What is the sum of the first 6 odd numbers (1 + 3 + 5 + …)? (a) 11 (b) 21 (c) 36 (d) 42
  26. 26.What is the sum of all the whole numbers from 1 to 93? (a) 8742 (b) 4372 (c) 4371 (d) 4278
  27. 27.What is the sum of the first 11 terms of the AP 8, 11, 14, …? (a) 253 (b) 506 (c) 38 (d) 256
  28. 28.What is the 11th term of the AP 15, 20, 25, 30, …? (a) 50 (b) 65 (c) 70 (d) 55
  29. 29.What is the sum of the first 9 odd numbers (1 + 3 + 5 + …)? (a) 45 (b) 17 (c) 81 (d) 90
  30. 30.What is the sum of the first 9 terms of the AP 8, 13, 18, …? (a) 48 (b) 252 (c) 257 (d) 504
  31. 31.What is the sum of the first 7 terms of the AP 9, 11, 13, …? (a) 210 (b) 21 (c) 112 (d) 105
  32. 32.What is the missing term in the AP 10, ?, 16, 19, 22? (a) 16 (b) 12 (c) 14 (d) 13
  33. 33.What is the 39th term of the AP 20, 26, 32, 38, …? (a) 228 (b) 248 (c) 234 (d) 254
  34. 34.What is the sum of the first 10 terms of the AP 7, 8, 9, …? (a) 115 (b) 16 (c) 230 (d) 120
  35. 35.What is the 40th term of the AP 18, 25, 32, 39, …? (a) 273 (b) 298 (c) 291 (d) 280
  36. 36.What is the sum of the first 6 terms of the AP 7, 11, 15, …? (a) 114 (b) 102 (c) 204 (d) 27
  37. 37.What is the sum of the first 9 terms of the AP 9, 15, 21, …? (a) 594 (b) 297 (c) 324 (d) 57
  38. 38.What is the sum of all the whole numbers from 1 to 65? (a) 4290 (b) 2145 (c) 2146 (d) 2080
  39. 39.What is the 29th term of the AP 12, 17, 22, 27, …? (a) 145 (b) 140 (c) 152 (d) 157
  40. 40.What is the missing term in the AP 6, ?, 10, 12, 14? (a) 7 (b) 8 (c) 9 (d) 10

Answer key

  1. 153
  2. 81
  3. 41
  4. 190
  5. 1378
  6. 35
  7. 90
  8. 231
  9. 175
  10. 10th
  11. 40th
  12. 113
  13. 234
  14. 110
  15. 114
  16. 68
  17. 115
  18. 200
  19. 279
  20. 441
  21. 286
  22. 25
  23. 168
  24. 15th
  25. 36
  26. 4371
  27. 253
  28. 65
  29. 81
  30. 252
  31. 105
  32. 13
  33. 248
  34. 115
  35. 291
  36. 102
  37. 297
  38. 2145
  39. 152
  40. 8

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