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Arithmetic Progression Worksheet for Olympiad

Maths Olympiad topic 29: Sequences and AP · Set 255 · 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 17, 21, 25, 29, …? (a) 73 (b) 60 (c) 56 (d) 77
  2. 2.What is the 14th term of the AP 6, 14, 22, 30, …? (a) 110 (b) 118 (c) 112 (d) 104
  3. 3.What is the sum of all the whole numbers from 1 to 52? (a) 1326 (b) 1378 (c) 2756 (d) 1352
  4. 4.What is the sum of the first 16 odd numbers (1 + 3 + 5 + …)? (a) 256 (b) 272 (c) 31 (d) 136
  5. 5.What is the sum of the first 6 terms of the AP 7, 11, 15, …? (a) 27 (b) 204 (c) 114 (d) 102
  6. 6.What is the sum of the first 8 terms of the AP 4, 10, 16, …? (a) 46 (b) 224 (c) 400 (d) 200
  7. 7.What is the sum of all the whole numbers from 1 to 28? (a) 378 (b) 406 (c) 812 (d) 392
  8. 8.What is the sum of the first 7 odd numbers (1 + 3 + 5 + …)? (a) 49 (b) 13 (c) 28 (d) 56
  9. 9.What is the 14th term of the AP 19, 25, 31, 37, …? (a) 78 (b) 97 (c) 103 (d) 84
  10. 10.Which term of the AP 19, 22, 25, 28, … is 67? (a) 18th (b) 16th (c) 19th (d) 17th
  11. 11.What is the 29th term of the AP 6, 15, 24, 33, …? (a) 267 (b) 252 (c) 261 (d) 258
  12. 12.What is the sum of the first 7 terms of the AP 9, 11, 13, …? (a) 21 (b) 112 (c) 105 (d) 210
  13. 13.What is the 13th term of the AP 19, 28, 37, 46, …? (a) 117 (b) 127 (c) 108 (d) 136
  14. 14.What is the sum of all the whole numbers from 1 to 60? (a) 1800 (b) 1770 (c) 3660 (d) 1830
  15. 15.What is the sum of the first 6 terms of the AP 10, 13, 16, …? (a) 25 (b) 210 (c) 105 (d) 114
  16. 16.What is the 10th term of the AP 16, 19, 22, 25, …? (a) 30 (b) 43 (c) 27 (d) 46
  17. 17.What is the sum of the first 6 odd numbers (1 + 3 + 5 + …)? (a) 42 (b) 11 (c) 21 (d) 36
  18. 18.What is the missing term in the AP 9, 16, ?, 30, 37? (a) 22 (b) 30 (c) 23 (d) 24
  19. 19.What is the 31st term of the AP 6, 10, 14, 18, …? (a) 120 (b) 124 (c) 130 (d) 126
  20. 20.What is the 24th term of the AP 16, 24, 32, 40, …? (a) 200 (b) 208 (c) 184 (d) 192
  21. 21.What is the 36th term of the AP 11, 15, 19, 23, …? (a) 144 (b) 155 (c) 140 (d) 151
  22. 22.What is the sum of the first 6 terms of the AP 2, 8, 14, …? (a) 102 (b) 32 (c) 204 (d) 120
  23. 23.What is the sum of all the whole numbers from 1 to 11? (a) 67 (b) 55 (c) 66 (d) 132
  24. 24.Which term of the AP 20, 23, 26, 29, … is 59? (a) 14th (b) 15th (c) 16th (d) 13th
  25. 25.What is the sum of the first 18 odd numbers (1 + 3 + 5 + …)? (a) 324 (b) 171 (c) 342 (d) 35
  26. 26.What is the 14th term of the AP 10, 13, 16, 19, …? (a) 42 (b) 39 (c) 52 (d) 49
  27. 27.What is the sum of the first 9 terms of the AP 6, 7, 8, …? (a) 180 (b) 14 (c) 90 (d) 91
  28. 28.What is the 28th term of the AP 14, 22, 30, 38, …? (a) 230 (b) 238 (c) 216 (d) 224
  29. 29.What is the sum of the first 10 terms of the AP 9, 11, 13, …? (a) 27 (b) 180 (c) 190 (d) 360
  30. 30.What is the sum of the first 19 odd numbers (1 + 3 + 5 + …)? (a) 37 (b) 380 (c) 190 (d) 361
  31. 31.What is the sum of the first 11 terms of the AP 6, 7, 8, …? (a) 122 (b) 121 (c) 242 (d) 16
  32. 32.What is the missing term in the AP 2, 11, ?, 29, 38? (a) 21 (b) 29 (c) 20 (d) 19
  33. 33.What is the sum of the first 9 terms of the AP 1, 4, 7, …? (a) 25 (b) 120 (c) 234 (d) 117
  34. 34.What is the sum of all the whole numbers from 1 to 32? (a) 528 (b) 1056 (c) 496 (d) 512
  35. 35.What is the sum of all the whole numbers from 1 to 68? (a) 4692 (b) 2346 (c) 2278 (d) 2312
  36. 36.What is the 20th term of the AP 12, 15, 18, 21, …? (a) 60 (b) 72 (c) 57 (d) 69
  37. 37.What is the missing term in the AP 2, 4, 6, ?, 10? (a) 10 (b) 8 (c) 9 (d) 7
  38. 38.What is the 33rd term of the AP 2, 11, 20, 29, …? (a) 288 (b) 299 (c) 297 (d) 290
  39. 39.What is the sum of the first 24 odd numbers (1 + 3 + 5 + …)? (a) 576 (b) 600 (c) 300 (d) 47
  40. 40.What is the 20th term of the AP 2, 6, 10, 14, …? (a) 82 (b) 78 (c) 80 (d) 76

Answer key

  1. 73
  2. 110
  3. 1378
  4. 256
  5. 102
  6. 200
  7. 406
  8. 49
  9. 97
  10. 17th
  11. 258
  12. 105
  13. 127
  14. 1830
  15. 105
  16. 43
  17. 36
  18. 23
  19. 126
  20. 200
  21. 151
  22. 102
  23. 66
  24. 14th
  25. 324
  26. 49
  27. 90
  28. 230
  29. 180
  30. 361
  31. 121
  32. 20
  33. 117
  34. 528
  35. 2346
  36. 69
  37. 8
  38. 290
  39. 576
  40. 78

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