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Arithmetic Progression Worksheet for Olympiad

Maths Olympiad topic 29: Sequences and AP · Set 314 · 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 the first 21 odd numbers (1 + 3 + 5 + …)? (a) 41 (b) 462 (c) 441 (d) 231
  2. 2.What is the sum of the first 16 odd numbers (1 + 3 + 5 + …)? (a) 272 (b) 136 (c) 31 (d) 256
  3. 3.What is the sum of all the whole numbers from 1 to 39? (a) 781 (b) 780 (c) 741 (d) 1560
  4. 4.What is the 29th term of the AP 2, 11, 20, 29, …? (a) 261 (b) 263 (c) 254 (d) 252
  5. 5.What is the sum of the first 11 terms of the AP 9, 14, 19, …? (a) 59 (b) 748 (c) 379 (d) 374
  6. 6.What is the sum of the first 9 terms of the AP 1, 2, 3, …? (a) 90 (b) 9 (c) 45 (d) 46
  7. 7.What is the sum of the first 7 terms of the AP 10, 15, 20, …? (a) 40 (b) 180 (c) 350 (d) 175
  8. 8.What is the sum of all the whole numbers from 1 to 23? (a) 552 (b) 276 (c) 253 (d) 277
  9. 9.What is the 27th term of the AP 14, 20, 26, 32, …? (a) 170 (b) 162 (c) 156 (d) 176
  10. 10.What is the sum of the first 8 odd numbers (1 + 3 + 5 + …)? (a) 15 (b) 64 (c) 36 (d) 72
  11. 11.What is the 37th term of the AP 3, 11, 19, 27, …? (a) 299 (b) 288 (c) 291 (d) 296
  12. 12.What is the sum of the first 7 terms of the AP 5, 9, 13, …? (a) 119 (b) 29 (c) 133 (d) 238
  13. 13.What is the sum of the first 8 terms of the AP 8, 10, 12, …? (a) 120 (b) 128 (c) 240 (d) 22
  14. 14.What is the missing term in the AP 6, 8, 10, ?, 14? (a) 14 (b) 13 (c) 12 (d) 11
  15. 15.What is the sum of the first 5 terms of the AP 2, 8, 14, …? (a) 70 (b) 26 (c) 85 (d) 140
  16. 16.What is the sum of all the whole numbers from 1 to 75? (a) 5700 (b) 2775 (c) 2851 (d) 2850
  17. 17.Which term of the AP 11, 18, 25, 32, … is 95? (a) 15th (b) 12th (c) 14th (d) 13th
  18. 18.What is the 13th term of the AP 5, 13, 21, 29, …? (a) 104 (b) 109 (c) 96 (d) 101
  19. 19.What is the 31st term of the AP 12, 19, 26, 33, …? (a) 217 (b) 210 (c) 222 (d) 229
  20. 20.What is the sum of all the whole numbers from 1 to 21? (a) 231 (b) 462 (c) 210 (d) 232
  21. 21.What is the missing term in the AP 6, 8, ?, 12, 14? (a) 9 (b) 11 (c) 10 (d) 12
  22. 22.What is the missing term in the AP 6, 10, ?, 18, 22? (a) 15 (b) 13 (c) 14 (d) 18
  23. 23.Which term of the AP 9, 17, 25, 33, … is 113? (a) 16th (b) 14th (c) 13th (d) 15th
  24. 24.What is the 24th term of the AP 10, 12, 14, 16, …? (a) 58 (b) 56 (c) 48 (d) 46
  25. 25.What is the sum of all the whole numbers from 1 to 66? (a) 4422 (b) 2145 (c) 2178 (d) 2211
  26. 26.What is the 36th term of the AP 8, 15, 22, 29, …? (a) 253 (b) 252 (c) 245 (d) 260
  27. 27.What is the 28th term of the AP 13, 16, 19, 22, …? (a) 84 (b) 81 (c) 94 (d) 97
  28. 28.What is the 38th term of the AP 11, 18, 25, 32, …? (a) 270 (b) 259 (c) 266 (d) 277
  29. 29.What is the sum of the first 9 terms of the AP 9, 15, 21, …? (a) 297 (b) 57 (c) 594 (d) 324
  30. 30.What is the missing term in the AP 9, ?, 13, 15, 17? (a) 12 (b) 13 (c) 11 (d) 10
  31. 31.What is the 36th term of the AP 6, 8, 10, 12, …? (a) 70 (b) 72 (c) 78 (d) 76
  32. 32.What is the sum of the first 12 terms of the AP 9, 11, 13, …? (a) 31 (b) 252 (c) 480 (d) 240
  33. 33.What is the 23rd term of the AP 2, 5, 8, 11, …? (a) 66 (b) 69 (c) 68 (d) 71
  34. 34.What is the sum of the first 5 terms of the AP 4, 10, 16, …? (a) 28 (b) 95 (c) 160 (d) 80
  35. 35.What is the missing term in the AP 5, 13, ?, 29, 37? (a) 22 (b) 29 (c) 20 (d) 21
  36. 36.What is the 34th term of the AP 20, 24, 28, 32, …? (a) 132 (b) 152 (c) 136 (d) 156
  37. 37.What is the sum of the first 18 odd numbers (1 + 3 + 5 + …)? (a) 342 (b) 324 (c) 35 (d) 171
  38. 38.What is the sum of all the whole numbers from 1 to 99? (a) 9900 (b) 4951 (c) 4950 (d) 4851
  39. 39.What is the 12th term of the AP 17, 20, 23, 26, …? (a) 53 (b) 33 (c) 50 (d) 36
  40. 40.Which term of the AP 20, 24, 28, 32, … is 160? (a) 37th (b) 36th (c) 35th (d) 40th

Answer key

  1. 441
  2. 256
  3. 780
  4. 254
  5. 374
  6. 45
  7. 175
  8. 276
  9. 170
  10. 64
  11. 291
  12. 119
  13. 120
  14. 12
  15. 70
  16. 2850
  17. 13th
  18. 101
  19. 222
  20. 231
  21. 10
  22. 14
  23. 14th
  24. 56
  25. 2211
  26. 253
  27. 94
  28. 270
  29. 297
  30. 11
  31. 76
  32. 240
  33. 68
  34. 80
  35. 21
  36. 152
  37. 324
  38. 4950
  39. 50
  40. 36th

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