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Arithmetic Progression Worksheet for Olympiad

Maths Olympiad topic 29: Sequences and AP · Set 222 · 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 17th term of the AP 7, 15, 23, 31, …? (a) 143 (b) 128 (c) 135 (d) 136
  2. 2.What is the sum of the first 6 terms of the AP 1, 3, 5, …? (a) 36 (b) 42 (c) 72 (d) 11
  3. 3.What is the 22nd term of the AP 8, 11, 14, 17, …? (a) 71 (b) 63 (c) 66 (d) 74
  4. 4.What is the missing term in the AP 8, ?, 24, 32, 40? (a) 17 (b) 24 (c) 15 (d) 16
  5. 5.Which term of the AP 3, 9, 15, 21, … is 153? (a) 28th (b) 25th (c) 26th (d) 27th
  6. 6.What is the sum of all the whole numbers from 1 to 39? (a) 780 (b) 781 (c) 1560 (d) 741
  7. 7.What is the 24th term of the AP 6, 13, 20, 27, …? (a) 161 (b) 168 (c) 167 (d) 174
  8. 8.What is the sum of the first 9 terms of the AP 5, 11, 17, …? (a) 288 (b) 522 (c) 261 (d) 53
  9. 9.What is the 36th term of the AP 20, 26, 32, 38, …? (a) 216 (b) 236 (c) 230 (d) 210
  10. 10.What is the sum of the first 9 terms of the AP 5, 9, 13, …? (a) 207 (b) 189 (c) 378 (d) 37
  11. 11.What is the 27th term of the AP 15, 20, 25, 30, …? (a) 150 (b) 145 (c) 135 (d) 130
  12. 12.What is the sum of the first 5 terms of the AP 7, 13, 19, …? (a) 190 (b) 31 (c) 110 (d) 95
  13. 13.What is the sum of the first 5 terms of the AP 4, 5, 6, …? (a) 8 (b) 30 (c) 31 (d) 60
  14. 14.What is the sum of the first 9 terms of the AP 5, 10, 15, …? (a) 225 (b) 45 (c) 450 (d) 230
  15. 15.What is the 37th term of the AP 2, 11, 20, 29, …? (a) 333 (b) 326 (c) 335 (d) 324
  16. 16.What is the sum of all the whole numbers from 1 to 24? (a) 276 (b) 600 (c) 288 (d) 300
  17. 17.Which term of the AP 7, 13, 19, 25, … is 181? (a) 31st (b) 32nd (c) 30th (d) 29th
  18. 18.What is the sum of all the whole numbers from 1 to 52? (a) 1326 (b) 1352 (c) 1378 (d) 2756
  19. 19.What is the missing term in the AP 20, 22, ?, 26, 28? (a) 25 (b) 26 (c) 24 (d) 23
  20. 20.What is the 21st term of the AP 1, 7, 13, 19, …? (a) 126 (b) 121 (c) 120 (d) 127
  21. 21.What is the missing term in the AP 1, ?, 19, 28, 37? (a) 11 (b) 9 (c) 10 (d) 19
  22. 22.What is the sum of all the whole numbers from 1 to 14? (a) 98 (b) 105 (c) 210 (d) 91
  23. 23.What is the sum of the first 11 terms of the AP 10, 15, 20, …? (a) 385 (b) 60 (c) 770 (d) 390
  24. 24.What is the sum of the first 15 odd numbers (1 + 3 + 5 + …)? (a) 240 (b) 120 (c) 29 (d) 225
  25. 25.What is the sum of all the whole numbers from 1 to 31? (a) 992 (b) 496 (c) 497 (d) 465
  26. 26.What is the sum of the first 10 terms of the AP 4, 9, 14, …? (a) 530 (b) 290 (c) 49 (d) 265
  27. 27.What is the missing term in the AP 1, 8, 15, ?, 29? (a) 29 (b) 21 (c) 22 (d) 23
  28. 28.What is the 16th term of the AP 8, 13, 18, 23, …? (a) 88 (b) 80 (c) 75 (d) 83
  29. 29.What is the sum of all the whole numbers from 1 to 22? (a) 253 (b) 231 (c) 506 (d) 242
  30. 30.What is the sum of the first 6 terms of the AP 3, 5, 7, …? (a) 96 (b) 54 (c) 48 (d) 13
  31. 31.What is the 26th term of the AP 20, 22, 24, 26, …? (a) 72 (b) 70 (c) 50 (d) 52
  32. 32.What is the sum of the first 11 terms of the AP 7, 13, 19, …? (a) 814 (b) 440 (c) 407 (d) 67
  33. 33.What is the missing term in the AP 18, 26, 34, ?, 50? (a) 43 (b) 42 (c) 50 (d) 41
  34. 34.What is the missing term in the AP 6, ?, 12, 15, 18? (a) 9 (b) 8 (c) 10 (d) 12
  35. 35.What is the 35th term of the AP 10, 12, 14, 16, …? (a) 78 (b) 70 (c) 80 (d) 68
  36. 36.What is the sum of the first 17 odd numbers (1 + 3 + 5 + …)? (a) 153 (b) 33 (c) 289 (d) 306
  37. 37.What is the sum of the first 26 odd numbers (1 + 3 + 5 + …)? (a) 351 (b) 676 (c) 702 (d) 51
  38. 38.What is the sum of all the whole numbers from 1 to 48? (a) 2352 (b) 1176 (c) 1128 (d) 1152
  39. 39.What is the 12th term of the AP 15, 22, 29, 36, …? (a) 92 (b) 84 (c) 77 (d) 99
  40. 40.What is the sum of all the whole numbers from 1 to 33? (a) 528 (b) 562 (c) 561 (d) 1122

Answer key

  1. 135
  2. 36
  3. 71
  4. 16
  5. 26th
  6. 780
  7. 167
  8. 261
  9. 230
  10. 189
  11. 145
  12. 95
  13. 30
  14. 225
  15. 326
  16. 300
  17. 30th
  18. 1378
  19. 24
  20. 121
  21. 10
  22. 105
  23. 385
  24. 225
  25. 496
  26. 265
  27. 22
  28. 83
  29. 253
  30. 48
  31. 70
  32. 407
  33. 42
  34. 9
  35. 78
  36. 289
  37. 676
  38. 1176
  39. 92
  40. 561

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