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Arithmetic Progression Worksheet for Olympiad

Maths Olympiad topic 29: Sequences and AP · Set 52 · 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 18th term of the AP 14, 16, 18, 20, …? (a) 34 (b) 50 (c) 48 (d) 36
  2. 2.Which term of the AP 16, 22, 28, 34, … is 58? (a) 9th (b) 10th (c) 8th (d) 7th
  3. 3.What is the 40th term of the AP 12, 18, 24, 30, …? (a) 246 (b) 240 (c) 252 (d) 234
  4. 4.What is the missing term in the AP 11, 19, ?, 35, 43? (a) 27 (b) 35 (c) 26 (d) 28
  5. 5.What is the 10th term of the AP 9, 12, 15, 18, …? (a) 39 (b) 30 (c) 36 (d) 27
  6. 6.What is the 13th term of the AP 5, 9, 13, 17, …? (a) 53 (b) 48 (c) 57 (d) 52
  7. 7.What is the missing term in the AP 7, 15, ?, 31, 39? (a) 23 (b) 31 (c) 22 (d) 24
  8. 8.What is the sum of the first 26 odd numbers (1 + 3 + 5 + …)? (a) 51 (b) 351 (c) 676 (d) 702
  9. 9.What is the sum of all the whole numbers from 1 to 25? (a) 325 (b) 300 (c) 650 (d) 326
  10. 10.What is the sum of the first 5 terms of the AP 2, 5, 8, …? (a) 43 (b) 40 (c) 14 (d) 80
  11. 11.What is the sum of all the whole numbers from 1 to 31? (a) 465 (b) 992 (c) 496 (d) 497
  12. 12.What is the sum of the first 5 terms of the AP 2, 3, 4, …? (a) 20 (b) 21 (c) 40 (d) 6
  13. 13.What is the missing term in the AP 1, 3, 5, ?, 9? (a) 9 (b) 6 (c) 7 (d) 8
  14. 14.What is the 37th term of the AP 8, 14, 20, 26, …? (a) 222 (b) 230 (c) 224 (d) 216
  15. 15.What is the 20th term of the AP 5, 9, 13, 17, …? (a) 85 (b) 76 (c) 81 (d) 80
  16. 16.What is the sum of all the whole numbers from 1 to 71? (a) 2485 (b) 2556 (c) 5112 (d) 2557
  17. 17.What is the sum of the first 11 terms of the AP 9, 10, 11, …? (a) 19 (b) 308 (c) 155 (d) 154
  18. 18.What is the sum of all the whole numbers from 1 to 23? (a) 253 (b) 276 (c) 552 (d) 277
  19. 19.What is the sum of the first 5 terms of the AP 6, 10, 14, …? (a) 140 (b) 22 (c) 80 (d) 70
  20. 20.What is the sum of the first 6 terms of the AP 5, 8, 11, …? (a) 20 (b) 150 (c) 84 (d) 75
  21. 21.What is the sum of the first 9 terms of the AP 2, 3, 4, …? (a) 54 (b) 10 (c) 108 (d) 55
  22. 22.What is the sum of the first 10 terms of the AP 3, 4, 5, …? (a) 12 (b) 75 (c) 80 (d) 150
  23. 23.What is the 18th term of the AP 4, 6, 8, 10, …? (a) 36 (b) 38 (c) 40 (d) 34
  24. 24.What is the sum of the first 7 odd numbers (1 + 3 + 5 + …)? (a) 56 (b) 13 (c) 28 (d) 49
  25. 25.What is the 28th term of the AP 13, 15, 17, 19, …? (a) 67 (b) 56 (c) 69 (d) 54
  26. 26.What is the 21st term of the AP 13, 21, 29, 37, …? (a) 160 (b) 181 (c) 173 (d) 168
  27. 27.What is the 15th term of the AP 15, 20, 25, 30, …? (a) 85 (b) 90 (c) 75 (d) 70
  28. 28.What is the sum of all the whole numbers from 1 to 24? (a) 288 (b) 600 (c) 276 (d) 300
  29. 29.What is the sum of the first 7 terms of the AP 4, 7, 10, …? (a) 91 (b) 182 (c) 22 (d) 94
  30. 30.What is the sum of all the whole numbers from 1 to 86? (a) 7482 (b) 3655 (c) 3698 (d) 3741
  31. 31.What is the 18th term of the AP 6, 10, 14, 18, …? (a) 72 (b) 78 (c) 68 (d) 74
  32. 32.What is the missing term in the AP 5, 12, ?, 26, 33? (a) 26 (b) 18 (c) 20 (d) 19
  33. 33.What is the sum of the first 19 odd numbers (1 + 3 + 5 + …)? (a) 37 (b) 361 (c) 190 (d) 380
  34. 34.What is the 33rd term of the AP 14, 16, 18, 20, …? (a) 80 (b) 78 (c) 66 (d) 64
  35. 35.What is the sum of the first 5 terms of the AP 6, 11, 16, …? (a) 26 (b) 85 (c) 80 (d) 160
  36. 36.What is the 12th term of the AP 15, 20, 25, 30, …? (a) 55 (b) 60 (c) 70 (d) 75
  37. 37.What is the missing term in the AP 12, 21, 30, ?, 48? (a) 38 (b) 48 (c) 39 (d) 40
  38. 38.What is the missing term in the AP 19, ?, 37, 46, 55? (a) 29 (b) 28 (c) 27 (d) 37
  39. 39.What is the 32nd term of the AP 19, 28, 37, 46, …? (a) 288 (b) 279 (c) 307 (d) 298
  40. 40.What is the sum of all the whole numbers from 1 to 55? (a) 1541 (b) 3080 (c) 1485 (d) 1540

Answer key

  1. 48
  2. 8th
  3. 246
  4. 27
  5. 36
  6. 53
  7. 23
  8. 676
  9. 325
  10. 40
  11. 496
  12. 20
  13. 7
  14. 224
  15. 81
  16. 2556
  17. 154
  18. 276
  19. 70
  20. 75
  21. 54
  22. 75
  23. 38
  24. 49
  25. 67
  26. 173
  27. 85
  28. 300
  29. 91
  30. 3741
  31. 74
  32. 19
  33. 361
  34. 78
  35. 80
  36. 70
  37. 39
  38. 28
  39. 298
  40. 1540

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