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Arithmetic Progression Worksheet for Olympiad

Maths Olympiad topic 29: Sequences and AP · Set 11 · 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 all the whole numbers from 1 to 43? (a) 903 (b) 946 (c) 947 (d) 1892
  2. 2.What is the sum of the first 16 odd numbers (1 + 3 + 5 + …)? (a) 272 (b) 31 (c) 136 (d) 256
  3. 3.What is the sum of the first 5 terms of the AP 8, 11, 14, …? (a) 73 (b) 140 (c) 20 (d) 70
  4. 4.What is the 24th term of the AP 16, 18, 20, 22, …? (a) 64 (b) 62 (c) 46 (d) 48
  5. 5.What is the sum of all the whole numbers from 1 to 41? (a) 861 (b) 862 (c) 820 (d) 1722
  6. 6.What is the 16th term of the AP 1, 4, 7, 10, …? (a) 48 (b) 46 (c) 45 (d) 49
  7. 7.What is the 32nd term of the AP 8, 17, 26, 35, …? (a) 287 (b) 279 (c) 296 (d) 288
  8. 8.What is the sum of the first 11 terms of the AP 5, 11, 17, …? (a) 65 (b) 385 (c) 418 (d) 770
  9. 9.What is the 19th term of the AP 16, 24, 32, 40, …? (a) 160 (b) 144 (c) 168 (d) 152
  10. 10.What is the 33rd term of the AP 14, 23, 32, 41, …? (a) 302 (b) 311 (c) 288 (d) 297
  11. 11.What is the missing term in the AP 12, 16, ?, 24, 28? (a) 20 (b) 19 (c) 24 (d) 21
  12. 12.What is the missing term in the AP 6, 9, 12, ?, 18? (a) 16 (b) 15 (c) 14 (d) 18
  13. 13.What is the sum of the first 10 terms of the AP 4, 10, 16, …? (a) 340 (b) 58 (c) 310 (d) 620
  14. 14.What is the sum of all the whole numbers from 1 to 23? (a) 552 (b) 253 (c) 277 (d) 276
  15. 15.What is the sum of all the whole numbers from 1 to 13? (a) 91 (b) 78 (c) 92 (d) 182
  16. 16.What is the sum of all the whole numbers from 1 to 85? (a) 3656 (b) 7310 (c) 3655 (d) 3570
  17. 17.What is the sum of all the whole numbers from 1 to 95? (a) 9120 (b) 4561 (c) 4465 (d) 4560
  18. 18.What is the 13th term of the AP 13, 19, 25, 31, …? (a) 85 (b) 78 (c) 91 (d) 72
  19. 19.What is the sum of the first 25 odd numbers (1 + 3 + 5 + …)? (a) 49 (b) 650 (c) 325 (d) 625
  20. 20.Which term of the AP 20, 26, 32, 38, … is 188? (a) 28th (b) 31st (c) 30th (d) 29th
  21. 21.What is the sum of all the whole numbers from 1 to 49? (a) 1176 (b) 2450 (c) 1225 (d) 1226
  22. 22.What is the 24th term of the AP 8, 17, 26, 35, …? (a) 216 (b) 215 (c) 224 (d) 207
  23. 23.What is the sum of the first 10 terms of the AP 2, 8, 14, …? (a) 56 (b) 580 (c) 320 (d) 290
  24. 24.What is the sum of the first 12 terms of the AP 9, 11, 13, …? (a) 31 (b) 240 (c) 252 (d) 480
  25. 25.What is the 32nd term of the AP 11, 14, 17, 20, …? (a) 104 (b) 93 (c) 107 (d) 96
  26. 26.What is the missing term in the AP 8, 10, 12, ?, 16? (a) 15 (b) 16 (c) 13 (d) 14
  27. 27.What is the sum of the first 5 odd numbers (1 + 3 + 5 + …)? (a) 9 (b) 25 (c) 30 (d) 15
  28. 28.Which term of the AP 18, 21, 24, 27, … is 87? (a) 25th (b) 23rd (c) 29th (d) 24th
  29. 29.Which term of the AP 12, 20, 28, 36, … is 132? (a) 16th (b) 15th (c) 17th (d) 18th
  30. 30.What is the sum of the first 11 terms of the AP 3, 8, 13, …? (a) 616 (b) 308 (c) 53 (d) 313
  31. 31.What is the sum of the first 11 terms of the AP 9, 12, 15, …? (a) 39 (b) 264 (c) 267 (d) 528
  32. 32.What is the sum of the first 21 odd numbers (1 + 3 + 5 + …)? (a) 441 (b) 231 (c) 41 (d) 462
  33. 33.What is the sum of the first 11 odd numbers (1 + 3 + 5 + …)? (a) 132 (b) 21 (c) 66 (d) 121
  34. 34.What is the missing term in the AP 5, 7, 9, ?, 13? (a) 13 (b) 10 (c) 12 (d) 11
  35. 35.What is the sum of the first 12 odd numbers (1 + 3 + 5 + …)? (a) 23 (b) 144 (c) 156 (d) 78
  36. 36.What is the 30th term of the AP 14, 17, 20, 23, …? (a) 87 (b) 101 (c) 104 (d) 90
  37. 37.What is the 19th term of the AP 17, 19, 21, 23, …? (a) 55 (b) 38 (c) 36 (d) 53
  38. 38.What is the 16th term of the AP 20, 27, 34, 41, …? (a) 105 (b) 125 (c) 132 (d) 112
  39. 39.Which term of the AP 13, 21, 29, 37, … is 213? (a) 27th (b) 25th (c) 26th (d) 28th
  40. 40.What is the 16th term of the AP 5, 8, 11, 14, …? (a) 53 (b) 48 (c) 45 (d) 50

Answer key

  1. 946
  2. 256
  3. 70
  4. 62
  5. 861
  6. 46
  7. 287
  8. 385
  9. 160
  10. 302
  11. 20
  12. 15
  13. 310
  14. 276
  15. 91
  16. 3655
  17. 4560
  18. 85
  19. 625
  20. 29th
  21. 1225
  22. 215
  23. 290
  24. 240
  25. 104
  26. 14
  27. 25
  28. 24th
  29. 16th
  30. 308
  31. 264
  32. 441
  33. 121
  34. 11
  35. 144
  36. 101
  37. 53
  38. 125
  39. 26th
  40. 50

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