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Arithmetic Progression Worksheet for Olympiad

Maths Olympiad topic 29: Sequences and AP · Set 174 · 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 missing term in the AP 13, 21, 29, ?, 45? (a) 38 (b) 36 (c) 37 (d) 45
  2. 2.What is the 16th term of the AP 17, 20, 23, 26, …? (a) 65 (b) 48 (c) 62 (d) 45
  3. 3.What is the sum of all the whole numbers from 1 to 16? (a) 272 (b) 128 (c) 136 (d) 120
  4. 4.What is the 35th term of the AP 11, 20, 29, 38, …? (a) 326 (b) 315 (c) 317 (d) 306
  5. 5.What is the 18th term of the AP 15, 21, 27, 33, …? (a) 117 (b) 108 (c) 123 (d) 102
  6. 6.What is the sum of the first 8 odd numbers (1 + 3 + 5 + …)? (a) 64 (b) 15 (c) 36 (d) 72
  7. 7.What is the 34th term of the AP 3, 8, 13, 18, …? (a) 165 (b) 170 (c) 168 (d) 173
  8. 8.What is the missing term in the AP 8, ?, 14, 17, 20? (a) 10 (b) 12 (c) 11 (d) 14
  9. 9.What is the sum of all the whole numbers from 1 to 48? (a) 1128 (b) 2352 (c) 1152 (d) 1176
  10. 10.What is the sum of all the whole numbers from 1 to 91? (a) 4186 (b) 4187 (c) 4095 (d) 8372
  11. 11.What is the 36th term of the AP 3, 11, 19, 27, …? (a) 288 (b) 291 (c) 280 (d) 283
  12. 12.Which term of the AP 11, 14, 17, 20, … is 32? (a) 9th (b) 7th (c) 10th (d) 8th
  13. 13.What is the sum of the first 6 terms of the AP 6, 12, 18, …? (a) 252 (b) 144 (c) 126 (d) 36
  14. 14.What is the sum of the first 10 terms of the AP 6, 10, 14, …? (a) 42 (b) 240 (c) 480 (d) 260
  15. 15.Which term of the AP 8, 16, 24, 32, … is 288? (a) 35th (b) 38th (c) 37th (d) 36th
  16. 16.What is the sum of all the whole numbers from 1 to 63? (a) 4032 (b) 1953 (c) 2016 (d) 2017
  17. 17.What is the sum of the first 12 odd numbers (1 + 3 + 5 + …)? (a) 78 (b) 144 (c) 23 (d) 156
  18. 18.What is the 20th term of the AP 8, 17, 26, 35, …? (a) 188 (b) 171 (c) 180 (d) 179
  19. 19.What is the sum of all the whole numbers from 1 to 64? (a) 2016 (b) 2080 (c) 4160 (d) 2048
  20. 20.What is the 24th term of the AP 12, 21, 30, 39, …? (a) 219 (b) 207 (c) 216 (d) 228
  21. 21.What is the missing term in the AP 10, ?, 16, 19, 22? (a) 13 (b) 16 (c) 14 (d) 12
  22. 22.What is the missing term in the AP 8, 11, ?, 17, 20? (a) 15 (b) 13 (c) 17 (d) 14
  23. 23.What is the sum of the first 8 terms of the AP 2, 3, 4, …? (a) 48 (b) 9 (c) 88 (d) 44
  24. 24.What is the 27th term of the AP 17, 21, 25, 29, …? (a) 125 (b) 121 (c) 104 (d) 108
  25. 25.What is the missing term in the AP 6, ?, 16, 21, 26? (a) 11 (b) 16 (c) 12 (d) 10
  26. 26.What is the sum of all the whole numbers from 1 to 79? (a) 3161 (b) 6320 (c) 3160 (d) 3081
  27. 27.What is the 12th term of the AP 7, 15, 23, 31, …? (a) 103 (b) 88 (c) 96 (d) 95
  28. 28.What is the 37th term of the AP 11, 20, 29, 38, …? (a) 324 (b) 344 (c) 335 (d) 333
  29. 29.What is the sum of the first 9 terms of the AP 2, 5, 8, …? (a) 126 (b) 26 (c) 129 (d) 252
  30. 30.Which term of the AP 15, 18, 21, 24, … is 126? (a) 38th (b) 37th (c) 39th (d) 42nd
  31. 31.What is the 14th term of the AP 17, 25, 33, 41, …? (a) 129 (b) 121 (c) 112 (d) 104
  32. 32.What is the 12th term of the AP 2, 4, 6, 8, …? (a) 25 (b) 24 (c) 26 (d) 22
  33. 33.What is the 12th term of the AP 10, 15, 20, 25, …? (a) 65 (b) 60 (c) 55 (d) 70
  34. 34.Which term of the AP 20, 26, 32, 38, … is 146? (a) 21st (b) 23rd (c) 24th (d) 22nd
  35. 35.What is the missing term in the AP 18, 23, ?, 33, 38? (a) 29 (b) 33 (c) 27 (d) 28
  36. 36.What is the sum of the first 7 terms of the AP 10, 16, 22, …? (a) 196 (b) 392 (c) 46 (d) 217
  37. 37.What is the 13th term of the AP 10, 13, 16, 19, …? (a) 36 (b) 49 (c) 46 (d) 39
  38. 38.What is the sum of the first 12 terms of the AP 7, 10, 13, …? (a) 282 (b) 300 (c) 564 (d) 40
  39. 39.What is the 32nd term of the AP 17, 25, 33, 41, …? (a) 273 (b) 248 (c) 256 (d) 265
  40. 40.What is the sum of the first 12 terms of the AP 1, 6, 11, …? (a) 56 (b) 372 (c) 342 (d) 684

Answer key

  1. 37
  2. 62
  3. 136
  4. 317
  5. 117
  6. 64
  7. 168
  8. 11
  9. 1176
  10. 4186
  11. 283
  12. 8th
  13. 126
  14. 240
  15. 36th
  16. 2016
  17. 144
  18. 179
  19. 2080
  20. 219
  21. 13
  22. 14
  23. 44
  24. 121
  25. 11
  26. 3160
  27. 95
  28. 335
  29. 126
  30. 38th
  31. 121
  32. 24
  33. 65
  34. 22nd
  35. 28
  36. 196
  37. 46
  38. 282
  39. 265
  40. 342

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