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Arithmetic Progression Worksheet for Olympiad

Maths Olympiad topic 29: Sequences and AP · Set 202 · 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 15th term of the AP 11, 16, 21, 26, …? (a) 81 (b) 86 (c) 75 (d) 70
  2. 2.What is the sum of all the whole numbers from 1 to 24? (a) 300 (b) 288 (c) 600 (d) 276
  3. 3.What is the sum of the first 7 odd numbers (1 + 3 + 5 + …)? (a) 56 (b) 13 (c) 49 (d) 28
  4. 4.What is the 33rd term of the AP 20, 27, 34, 41, …? (a) 251 (b) 231 (c) 244 (d) 224
  5. 5.What is the 29th term of the AP 15, 18, 21, 24, …? (a) 102 (b) 84 (c) 99 (d) 87
  6. 6.What is the missing term in the AP 5, 13, ?, 29, 37? (a) 21 (b) 20 (c) 29 (d) 22
  7. 7.What is the missing term in the AP 12, 17, 22, ?, 32? (a) 27 (b) 32 (c) 26 (d) 28
  8. 8.What is the sum of the first 18 odd numbers (1 + 3 + 5 + …)? (a) 35 (b) 171 (c) 342 (d) 324
  9. 9.What is the sum of the first 15 odd numbers (1 + 3 + 5 + …)? (a) 225 (b) 29 (c) 120 (d) 240
  10. 10.What is the 17th term of the AP 12, 19, 26, 33, …? (a) 119 (b) 112 (c) 131 (d) 124
  11. 11.What is the 22nd term of the AP 3, 11, 19, 27, …? (a) 168 (b) 176 (c) 171 (d) 179
  12. 12.What is the missing term in the AP 13, ?, 21, 25, 29? (a) 18 (b) 17 (c) 21 (d) 16
  13. 13.Which term of the AP 11, 13, 15, 17, … is 51? (a) 21st (b) 22nd (c) 23rd (d) 20th
  14. 14.What is the sum of all the whole numbers from 1 to 61? (a) 1830 (b) 1892 (c) 3782 (d) 1891
  15. 15.What is the sum of all the whole numbers from 1 to 40? (a) 780 (b) 800 (c) 1640 (d) 820
  16. 16.What is the sum of the first 9 terms of the AP 4, 5, 6, …? (a) 144 (b) 12 (c) 73 (d) 72
  17. 17.What is the sum of the first 10 odd numbers (1 + 3 + 5 + …)? (a) 55 (b) 19 (c) 100 (d) 110
  18. 18.What is the sum of the first 16 odd numbers (1 + 3 + 5 + …)? (a) 272 (b) 136 (c) 256 (d) 31
  19. 19.What is the sum of the first 11 terms of the AP 8, 11, 14, …? (a) 253 (b) 256 (c) 38 (d) 506
  20. 20.What is the 14th term of the AP 13, 17, 21, 25, …? (a) 56 (b) 52 (c) 65 (d) 69
  21. 21.What is the 38th term of the AP 1, 10, 19, 28, …? (a) 333 (b) 342 (c) 343 (d) 334
  22. 22.What is the sum of the first 12 odd numbers (1 + 3 + 5 + …)? (a) 156 (b) 78 (c) 144 (d) 23
  23. 23.What is the missing term in the AP 3, 11, 19, ?, 35? (a) 26 (b) 27 (c) 35 (d) 28
  24. 24.What is the 26th term of the AP 18, 20, 22, 24, …? (a) 52 (b) 50 (c) 68 (d) 70
  25. 25.What is the 34th term of the AP 3, 11, 19, 27, …? (a) 267 (b) 272 (c) 264 (d) 275
  26. 26.What is the sum of the first 7 terms of the AP 8, 13, 18, …? (a) 322 (b) 161 (c) 166 (d) 38
  27. 27.What is the sum of all the whole numbers from 1 to 59? (a) 1770 (b) 1771 (c) 1711 (d) 3540
  28. 28.What is the sum of the first 17 odd numbers (1 + 3 + 5 + …)? (a) 33 (b) 306 (c) 153 (d) 289
  29. 29.What is the sum of the first 6 terms of the AP 7, 8, 9, …? (a) 114 (b) 57 (c) 60 (d) 12
  30. 30.What is the sum of the first 10 terms of the AP 2, 5, 8, …? (a) 155 (b) 310 (c) 29 (d) 170
  31. 31.What is the sum of all the whole numbers from 1 to 93? (a) 4278 (b) 4372 (c) 4371 (d) 8742
  32. 32.Which term of the AP 1, 9, 17, 25, … is 225? (a) 29th (b) 31st (c) 28th (d) 30th
  33. 33.What is the sum of the first 6 terms of the AP 2, 5, 8, …? (a) 66 (b) 57 (c) 17 (d) 114
  34. 34.Which term of the AP 3, 9, 15, 21, … is 237? (a) 41st (b) 39th (c) 42nd (d) 40th
  35. 35.What is the 36th term of the AP 9, 13, 17, 21, …? (a) 149 (b) 144 (c) 153 (d) 140
  36. 36.Which term of the AP 3, 8, 13, 18, … is 98? (a) 20th (b) 21st (c) 19th (d) 22nd
  37. 37.What is the 21st term of the AP 13, 21, 29, 37, …? (a) 160 (b) 168 (c) 181 (d) 173
  38. 38.What is the 31st term of the AP 16, 23, 30, 37, …? (a) 210 (b) 217 (c) 233 (d) 226
  39. 39.What is the missing term in the AP 17, 23, ?, 35, 41? (a) 28 (b) 35 (c) 29 (d) 30
  40. 40.What is the sum of the first 9 terms of the AP 8, 12, 16, …? (a) 40 (b) 234 (c) 216 (d) 432

Answer key

  1. 81
  2. 300
  3. 49
  4. 244
  5. 99
  6. 21
  7. 27
  8. 324
  9. 225
  10. 124
  11. 171
  12. 17
  13. 21st
  14. 1891
  15. 820
  16. 72
  17. 100
  18. 256
  19. 253
  20. 65
  21. 334
  22. 144
  23. 27
  24. 68
  25. 267
  26. 161
  27. 1770
  28. 289
  29. 57
  30. 155
  31. 4371
  32. 29th
  33. 57
  34. 40th
  35. 149
  36. 20th
  37. 173
  38. 226
  39. 29
  40. 216

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