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Arithmetic Progression Worksheet for Olympiad

Maths Olympiad topic 29: Sequences and AP · Set 215 · 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 18, 23, ?, 33, 38? (a) 27 (b) 33 (c) 29 (d) 28
  2. 2.What is the sum of the first 5 terms of the AP 8, 10, 12, …? (a) 120 (b) 16 (c) 65 (d) 60
  3. 3.What is the sum of the first 6 odd numbers (1 + 3 + 5 + …)? (a) 36 (b) 42 (c) 11 (d) 21
  4. 4.What is the sum of the first 8 terms of the AP 9, 13, 17, …? (a) 37 (b) 184 (c) 200 (d) 368
  5. 5.What is the 39th term of the AP 2, 4, 6, 8, …? (a) 76 (b) 78 (c) 80 (d) 79
  6. 6.What is the missing term in the AP 13, 20, 27, ?, 41? (a) 34 (b) 33 (c) 41 (d) 35
  7. 7.What is the 32nd term of the AP 8, 10, 12, 14, …? (a) 72 (b) 64 (c) 62 (d) 70
  8. 8.What is the missing term in the AP 20, ?, 24, 26, 28? (a) 21 (b) 24 (c) 22 (d) 23
  9. 9.What is the sum of the first 10 terms of the AP 7, 12, 17, …? (a) 590 (b) 320 (c) 52 (d) 295
  10. 10.What is the missing term in the AP 14, ?, 30, 38, 46? (a) 30 (b) 22 (c) 21 (d) 23
  11. 11.What is the 25th term of the AP 13, 17, 21, 25, …? (a) 96 (b) 100 (c) 113 (d) 109
  12. 12.Which term of the AP 12, 16, 20, 24, … is 148? (a) 35th (b) 36th (c) 37th (d) 34th
  13. 13.Which term of the AP 3, 10, 17, 24, … is 199? (a) 28th (b) 30th (c) 31st (d) 29th
  14. 14.Which term of the AP 11, 15, 19, 23, … is 55? (a) 14th (b) 12th (c) 11th (d) 13th
  15. 15.What is the sum of the first 11 terms of the AP 7, 8, 9, …? (a) 17 (b) 132 (c) 264 (d) 133
  16. 16.What is the sum of the first 18 odd numbers (1 + 3 + 5 + …)? (a) 35 (b) 171 (c) 342 (d) 324
  17. 17.What is the missing term in the AP 12, ?, 30, 39, 48? (a) 30 (b) 20 (c) 21 (d) 22
  18. 18.What is the sum of the first 10 terms of the AP 1, 3, 5, …? (a) 100 (b) 110 (c) 200 (d) 19
  19. 19.What is the sum of the first 10 terms of the AP 1, 6, 11, …? (a) 46 (b) 260 (c) 235 (d) 470
  20. 20.Which term of the AP 11, 16, 21, 26, … is 126? (a) 23rd (b) 25th (c) 24th (d) 26th
  21. 21.What is the sum of all the whole numbers from 1 to 11? (a) 67 (b) 55 (c) 66 (d) 132
  22. 22.What is the sum of the first 9 odd numbers (1 + 3 + 5 + …)? (a) 45 (b) 90 (c) 17 (d) 81
  23. 23.What is the sum of the first 8 terms of the AP 3, 5, 7, …? (a) 160 (b) 17 (c) 88 (d) 80
  24. 24.What is the 11th term of the AP 20, 23, 26, 29, …? (a) 30 (b) 50 (c) 53 (d) 33
  25. 25.What is the 31st term of the AP 13, 21, 29, 37, …? (a) 248 (b) 240 (c) 253 (d) 261
  26. 26.What is the sum of all the whole numbers from 1 to 26? (a) 351 (b) 338 (c) 325 (d) 702
  27. 27.What is the 23rd term of the AP 2, 9, 16, 23, …? (a) 154 (b) 156 (c) 163 (d) 161
  28. 28.What is the sum of the first 21 odd numbers (1 + 3 + 5 + …)? (a) 462 (b) 231 (c) 441 (d) 41
  29. 29.Which term of the AP 8, 17, 26, 35, … is 152? (a) 19th (b) 18th (c) 16th (d) 17th
  30. 30.What is the sum of the first 5 terms of the AP 1, 2, 3, …? (a) 30 (b) 15 (c) 5 (d) 16
  31. 31.What is the sum of the first 7 terms of the AP 8, 10, 12, …? (a) 105 (b) 20 (c) 98 (d) 196
  32. 32.Which term of the AP 14, 16, 18, 20, … is 68? (a) 28th (b) 27th (c) 29th (d) 34th
  33. 33.What is the sum of the first 7 odd numbers (1 + 3 + 5 + …)? (a) 13 (b) 56 (c) 49 (d) 28
  34. 34.What is the sum of the first 16 odd numbers (1 + 3 + 5 + …)? (a) 272 (b) 136 (c) 31 (d) 256
  35. 35.What is the sum of the first 12 terms of the AP 9, 12, 15, …? (a) 324 (b) 306 (c) 42 (d) 612
  36. 36.What is the sum of the first 5 terms of the AP 1, 3, 5, …? (a) 25 (b) 50 (c) 30 (d) 9
  37. 37.What is the 27th term of the AP 20, 28, 36, 44, …? (a) 236 (b) 216 (c) 228 (d) 208
  38. 38.What is the 31st term of the AP 10, 19, 28, 37, …? (a) 279 (b) 289 (c) 280 (d) 270
  39. 39.What is the 25th term of the AP 8, 10, 12, 14, …? (a) 48 (b) 50 (c) 56 (d) 58
  40. 40.What is the sum of the first 11 terms of the AP 4, 7, 10, …? (a) 212 (b) 418 (c) 209 (d) 34

Answer key

  1. 28
  2. 60
  3. 36
  4. 184
  5. 78
  6. 34
  7. 70
  8. 22
  9. 295
  10. 22
  11. 109
  12. 35th
  13. 29th
  14. 12th
  15. 132
  16. 324
  17. 21
  18. 100
  19. 235
  20. 24th
  21. 66
  22. 81
  23. 80
  24. 50
  25. 253
  26. 351
  27. 156
  28. 441
  29. 17th
  30. 15
  31. 98
  32. 28th
  33. 49
  34. 256
  35. 306
  36. 25
  37. 228
  38. 280
  39. 56
  40. 209

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