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Arithmetic Progression Worksheet for Olympiad

Maths Olympiad topic 29: Sequences and AP · Set 470 · 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 the first 5 terms of the AP 3, 9, 15, …? (a) 75 (b) 150 (c) 27 (d) 90
  2. 2.What is the sum of the first 11 odd numbers (1 + 3 + 5 + …)? (a) 121 (b) 21 (c) 132 (d) 66
  3. 3.What is the 22nd term of the AP 20, 24, 28, 32, …? (a) 108 (b) 104 (c) 84 (d) 88
  4. 4.Which term of the AP 16, 24, 32, 40, … is 80? (a) 11th (b) 9th (c) 10th (d) 8th
  5. 5.What is the sum of the first 6 odd numbers (1 + 3 + 5 + …)? (a) 42 (b) 21 (c) 36 (d) 11
  6. 6.What is the sum of the first 5 terms of the AP 8, 10, 12, …? (a) 60 (b) 65 (c) 16 (d) 120
  7. 7.What is the 13th term of the AP 10, 16, 22, 28, …? (a) 88 (b) 78 (c) 82 (d) 72
  8. 8.What is the missing term in the AP 19, 24, ?, 34, 39? (a) 28 (b) 34 (c) 29 (d) 30
  9. 9.What is the 18th term of the AP 9, 14, 19, 24, …? (a) 94 (b) 85 (c) 90 (d) 99
  10. 10.Which term of the AP 10, 17, 24, 31, … is 143? (a) 21st (b) 20th (c) 19th (d) 22nd
  11. 11.What is the 13th term of the AP 2, 5, 8, 11, …? (a) 39 (b) 36 (c) 41 (d) 38
  12. 12.What is the 36th term of the AP 3, 6, 9, 12, …? (a) 105 (b) 108 (c) 109 (d) 111
  13. 13.What is the 11th term of the AP 13, 22, 31, 40, …? (a) 103 (b) 99 (c) 90 (d) 112
  14. 14.What is the sum of all the whole numbers from 1 to 84? (a) 7140 (b) 3486 (c) 3570 (d) 3528
  15. 15.What is the sum of the first 10 terms of the AP 6, 12, 18, …? (a) 660 (b) 60 (c) 330 (d) 360
  16. 16.What is the missing term in the AP 12, 21, ?, 39, 48? (a) 30 (b) 39 (c) 31 (d) 29
  17. 17.What is the 16th term of the AP 12, 15, 18, 21, …? (a) 48 (b) 45 (c) 60 (d) 57
  18. 18.What is the 40th term of the AP 18, 21, 24, 27, …? (a) 117 (b) 138 (c) 120 (d) 135
  19. 19.What is the missing term in the AP 7, 10, ?, 16, 19? (a) 14 (b) 12 (c) 13 (d) 16
  20. 20.What is the sum of the first 9 terms of the AP 6, 11, 16, …? (a) 468 (b) 46 (c) 234 (d) 239
  21. 21.What is the sum of the first 10 terms of the AP 5, 8, 11, …? (a) 32 (b) 200 (c) 370 (d) 185
  22. 22.What is the 11th term of the AP 15, 18, 21, 24, …? (a) 33 (b) 45 (c) 30 (d) 48
  23. 23.What is the sum of the first 5 terms of the AP 2, 3, 4, …? (a) 40 (b) 6 (c) 21 (d) 20
  24. 24.What is the 31st term of the AP 14, 23, 32, 41, …? (a) 279 (b) 270 (c) 284 (d) 293
  25. 25.What is the 37th term of the AP 20, 26, 32, 38, …? (a) 222 (b) 216 (c) 236 (d) 242
  26. 26.What is the sum of the first 10 terms of the AP 7, 8, 9, …? (a) 16 (b) 120 (c) 115 (d) 230
  27. 27.What is the 35th term of the AP 2, 9, 16, 23, …? (a) 240 (b) 238 (c) 247 (d) 245
  28. 28.Which term of the AP 10, 15, 20, 25, … is 180? (a) 35th (b) 34th (c) 36th (d) 37th
  29. 29.What is the 10th term of the AP 20, 23, 26, 29, …? (a) 50 (b) 27 (c) 47 (d) 30
  30. 30.What is the 16th term of the AP 4, 8, 12, 16, …? (a) 60 (b) 68 (c) 64 (d) 65
  31. 31.What is the sum of the first 16 odd numbers (1 + 3 + 5 + …)? (a) 256 (b) 136 (c) 272 (d) 31
  32. 32.Which term of the AP 13, 16, 19, 22, … is 58? (a) 17th (b) 18th (c) 16th (d) 15th
  33. 33.What is the 15th term of the AP 13, 21, 29, 37, …? (a) 112 (b) 133 (c) 120 (d) 125
  34. 34.What is the sum of all the whole numbers from 1 to 24? (a) 288 (b) 276 (c) 300 (d) 600
  35. 35.Which term of the AP 4, 12, 20, 28, … is 124? (a) 16th (b) 18th (c) 17th (d) 15th
  36. 36.What is the sum of all the whole numbers from 1 to 81? (a) 6642 (b) 3322 (c) 3240 (d) 3321
  37. 37.Which term of the AP 10, 13, 16, 19, … is 61? (a) 19th (b) 20th (c) 17th (d) 18th
  38. 38.What is the missing term in the AP 6, ?, 10, 12, 14? (a) 9 (b) 7 (c) 8 (d) 10
  39. 39.What is the missing term in the AP 15, 17, 19, ?, 23? (a) 23 (b) 20 (c) 22 (d) 21
  40. 40.What is the 21st term of the AP 12, 16, 20, 24, …? (a) 84 (b) 80 (c) 92 (d) 96

Answer key

  1. 75
  2. 121
  3. 104
  4. 9th
  5. 36
  6. 60
  7. 82
  8. 29
  9. 94
  10. 20th
  11. 38
  12. 108
  13. 103
  14. 3570
  15. 330
  16. 30
  17. 57
  18. 135
  19. 13
  20. 234
  21. 185
  22. 45
  23. 20
  24. 284
  25. 236
  26. 115
  27. 240
  28. 35th
  29. 47
  30. 64
  31. 256
  32. 16th
  33. 125
  34. 300
  35. 16th
  36. 3321
  37. 18th
  38. 8
  39. 21
  40. 92

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