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Arithmetic Progression Worksheet for Olympiad

Maths Olympiad topic 29: Sequences and AP · Set 503 · 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 14, ?, 20, 23, 26? (a) 18 (b) 17 (c) 20 (d) 16
  2. 2.What is the 24th term of the AP 2, 5, 8, 11, …? (a) 72 (b) 69 (c) 71 (d) 74
  3. 3.What is the sum of the first 14 odd numbers (1 + 3 + 5 + …)? (a) 210 (b) 27 (c) 105 (d) 196
  4. 4.What is the 33rd term of the AP 7, 14, 21, 28, …? (a) 231 (b) 238 (c) 232 (d) 224
  5. 5.Which term of the AP 3, 9, 15, 21, … is 81? (a) 16th (b) 15th (c) 13th (d) 14th
  6. 6.What is the 17th term of the AP 3, 12, 21, 30, …? (a) 144 (b) 156 (c) 153 (d) 147
  7. 7.What is the sum of the first 10 terms of the AP 8, 14, 20, …? (a) 350 (b) 380 (c) 62 (d) 700
  8. 8.What is the sum of the first 11 terms of the AP 2, 7, 12, …? (a) 302 (b) 594 (c) 52 (d) 297
  9. 9.What is the 40th term of the AP 7, 9, 11, 13, …? (a) 85 (b) 78 (c) 87 (d) 80
  10. 10.What is the missing term in the AP 7, 9, 11, ?, 15? (a) 12 (b) 13 (c) 15 (d) 14
  11. 11.What is the sum of the first 29 odd numbers (1 + 3 + 5 + …)? (a) 870 (b) 57 (c) 435 (d) 841
  12. 12.What is the sum of the first 12 terms of the AP 5, 6, 7, …? (a) 126 (b) 132 (c) 16 (d) 252
  13. 13.What is the 40th term of the AP 1, 3, 5, 7, …? (a) 80 (b) 78 (c) 81 (d) 79
  14. 14.Which term of the AP 6, 13, 20, 27, … is 55? (a) 7th (b) 10th (c) 8th (d) 9th
  15. 15.What is the sum of the first 8 terms of the AP 7, 11, 15, …? (a) 184 (b) 168 (c) 336 (d) 35
  16. 16.What is the sum of the first 21 odd numbers (1 + 3 + 5 + …)? (a) 41 (b) 441 (c) 231 (d) 462
  17. 17.What is the 20th term of the AP 8, 15, 22, 29, …? (a) 148 (b) 141 (c) 140 (d) 133
  18. 18.What is the sum of all the whole numbers from 1 to 28? (a) 392 (b) 378 (c) 812 (d) 406
  19. 19.What is the sum of the first 10 terms of the AP 3, 9, 15, …? (a) 57 (b) 600 (c) 300 (d) 330
  20. 20.What is the 39th term of the AP 14, 23, 32, 41, …? (a) 351 (b) 365 (c) 356 (d) 342
  21. 21.Which term of the AP 14, 20, 26, 32, … is 56? (a) 7th (b) 9th (c) 10th (d) 8th
  22. 22.What is the sum of all the whole numbers from 1 to 56? (a) 1596 (b) 1540 (c) 1568 (d) 3192
  23. 23.What is the sum of the first 22 odd numbers (1 + 3 + 5 + …)? (a) 43 (b) 484 (c) 253 (d) 506
  24. 24.What is the sum of all the whole numbers from 1 to 33? (a) 562 (b) 1122 (c) 528 (d) 561
  25. 25.What is the sum of all the whole numbers from 1 to 52? (a) 1352 (b) 1378 (c) 1326 (d) 2756
  26. 26.What is the 37th term of the AP 9, 11, 13, 15, …? (a) 74 (b) 81 (c) 72 (d) 83
  27. 27.Which term of the AP 7, 13, 19, 25, … is 97? (a) 18th (b) 16th (c) 15th (d) 17th
  28. 28.What is the sum of the first 10 odd numbers (1 + 3 + 5 + …)? (a) 100 (b) 55 (c) 110 (d) 19
  29. 29.What is the 11th term of the AP 2, 7, 12, 17, …? (a) 52 (b) 55 (c) 50 (d) 57
  30. 30.What is the sum of the first 8 terms of the AP 2, 3, 4, …? (a) 48 (b) 88 (c) 9 (d) 44
  31. 31.What is the sum of the first 9 terms of the AP 3, 9, 15, …? (a) 270 (b) 243 (c) 486 (d) 51
  32. 32.What is the sum of the first 8 terms of the AP 7, 9, 11, …? (a) 112 (b) 21 (c) 224 (d) 120
  33. 33.What is the missing term in the AP 5, ?, 15, 20, 25? (a) 11 (b) 9 (c) 10 (d) 15
  34. 34.What is the 23rd term of the AP 8, 14, 20, 26, …? (a) 146 (b) 138 (c) 132 (d) 140
  35. 35.What is the sum of all the whole numbers from 1 to 25? (a) 300 (b) 325 (c) 650 (d) 326
  36. 36.What is the 17th term of the AP 14, 18, 22, 26, …? (a) 68 (b) 64 (c) 82 (d) 78
  37. 37.What is the sum of the first 8 terms of the AP 8, 14, 20, …? (a) 256 (b) 232 (c) 464 (d) 50
  38. 38.What is the 21st term of the AP 7, 10, 13, 16, …? (a) 70 (b) 60 (c) 67 (d) 63
  39. 39.What is the 12th term of the AP 7, 13, 19, 25, …? (a) 72 (b) 66 (c) 73 (d) 79
  40. 40.What is the sum of all the whole numbers from 1 to 48? (a) 1176 (b) 1128 (c) 1152 (d) 2352

Answer key

  1. 17
  2. 71
  3. 196
  4. 231
  5. 14th
  6. 147
  7. 350
  8. 297
  9. 85
  10. 13
  11. 841
  12. 126
  13. 79
  14. 8th
  15. 168
  16. 441
  17. 141
  18. 406
  19. 300
  20. 356
  21. 8th
  22. 1596
  23. 484
  24. 561
  25. 1378
  26. 81
  27. 16th
  28. 100
  29. 52
  30. 44
  31. 243
  32. 112
  33. 10
  34. 140
  35. 325
  36. 78
  37. 232
  38. 67
  39. 73
  40. 1176

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