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Arithmetic Progression Worksheet for Olympiad

Maths Olympiad topic 29: Sequences and AP · Set 587 · 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 47? (a) 1081 (b) 1128 (c) 2256 (d) 1129
  2. 2.What is the 18th term of the AP 12, 19, 26, 33, …? (a) 138 (b) 131 (c) 119 (d) 126
  3. 3.What is the sum of all the whole numbers from 1 to 72? (a) 2556 (b) 5256 (c) 2628 (d) 2592
  4. 4.What is the 32nd term of the AP 20, 25, 30, 35, …? (a) 160 (b) 180 (c) 155 (d) 175
  5. 5.What is the 12th term of the AP 17, 23, 29, 35, …? (a) 66 (b) 72 (c) 83 (d) 89
  6. 6.What is the sum of all the whole numbers from 1 to 40? (a) 800 (b) 820 (c) 1640 (d) 780
  7. 7.What is the sum of the first 8 terms of the AP 5, 6, 7, …? (a) 72 (b) 68 (c) 136 (d) 12
  8. 8.What is the sum of the first 10 terms of the AP 1, 6, 11, …? (a) 260 (b) 235 (c) 46 (d) 470
  9. 9.What is the 21st term of the AP 10, 15, 20, 25, …? (a) 110 (b) 100 (c) 115 (d) 105
  10. 10.What is the sum of the first 6 terms of the AP 5, 6, 7, …? (a) 45 (b) 90 (c) 48 (d) 10
  11. 11.What is the 28th term of the AP 13, 20, 27, 34, …? (a) 209 (b) 202 (c) 196 (d) 189
  12. 12.What is the sum of the first 8 odd numbers (1 + 3 + 5 + …)? (a) 72 (b) 15 (c) 36 (d) 64
  13. 13.What is the 16th term of the AP 5, 8, 11, 14, …? (a) 53 (b) 50 (c) 45 (d) 48
  14. 14.What is the missing term in the AP 6, 10, ?, 18, 22? (a) 15 (b) 13 (c) 18 (d) 14
  15. 15.What is the 20th term of the AP 1, 3, 5, 7, …? (a) 39 (b) 38 (c) 40 (d) 41
  16. 16.What is the missing term in the AP 5, ?, 19, 26, 33? (a) 19 (b) 12 (c) 11 (d) 13
  17. 17.Which term of the AP 11, 14, 17, 20, … is 68? (a) 20th (b) 22nd (c) 19th (d) 21st
  18. 18.What is the sum of the first 5 odd numbers (1 + 3 + 5 + …)? (a) 9 (b) 30 (c) 15 (d) 25
  19. 19.What is the sum of the first 30 odd numbers (1 + 3 + 5 + …)? (a) 465 (b) 59 (c) 900 (d) 930
  20. 20.What is the sum of the first 6 terms of the AP 8, 10, 12, …? (a) 84 (b) 78 (c) 156 (d) 18
  21. 21.What is the sum of the first 11 terms of the AP 4, 5, 6, …? (a) 14 (b) 198 (c) 100 (d) 99
  22. 22.What is the 16th term of the AP 19, 23, 27, 31, …? (a) 64 (b) 83 (c) 79 (d) 60
  23. 23.What is the sum of the first 6 terms of the AP 9, 15, 21, …? (a) 144 (b) 162 (c) 39 (d) 288
  24. 24.What is the 20th term of the AP 2, 9, 16, 23, …? (a) 135 (b) 140 (c) 133 (d) 142
  25. 25.Which term of the AP 2, 8, 14, 20, … is 98? (a) 17th (b) 19th (c) 18th (d) 16th
  26. 26.What is the sum of the first 5 terms of the AP 7, 10, 13, …? (a) 130 (b) 65 (c) 68 (d) 19
  27. 27.What is the sum of the first 5 terms of the AP 9, 12, 15, …? (a) 75 (b) 21 (c) 150 (d) 78
  28. 28.What is the sum of the first 6 terms of the AP 10, 11, 12, …? (a) 75 (b) 15 (c) 78 (d) 150
  29. 29.What is the 28th term of the AP 10, 18, 26, 34, …? (a) 234 (b) 216 (c) 226 (d) 224
  30. 30.What is the 22nd term of the AP 19, 28, 37, 46, …? (a) 217 (b) 189 (c) 198 (d) 208
  31. 31.What is the 13th term of the AP 11, 18, 25, 32, …? (a) 102 (b) 91 (c) 95 (d) 84
  32. 32.What is the sum of the first 9 terms of the AP 5, 11, 17, …? (a) 53 (b) 261 (c) 288 (d) 522
  33. 33.What is the sum of the first 6 terms of the AP 7, 11, 15, …? (a) 204 (b) 27 (c) 114 (d) 102
  34. 34.What is the missing term in the AP 8, 15, 22, ?, 36? (a) 29 (b) 28 (c) 36 (d) 30
  35. 35.What is the sum of all the whole numbers from 1 to 10? (a) 50 (b) 55 (c) 110 (d) 45
  36. 36.What is the sum of the first 16 odd numbers (1 + 3 + 5 + …)? (a) 256 (b) 136 (c) 272 (d) 31
  37. 37.What is the sum of the first 19 odd numbers (1 + 3 + 5 + …)? (a) 361 (b) 37 (c) 380 (d) 190
  38. 38.What is the sum of the first 8 terms of the AP 8, 11, 14, …? (a) 160 (b) 148 (c) 29 (d) 296
  39. 39.What is the sum of all the whole numbers from 1 to 37? (a) 703 (b) 666 (c) 704 (d) 1406
  40. 40.What is the missing term in the AP 2, 6, ?, 14, 18? (a) 9 (b) 14 (c) 10 (d) 11

Answer key

  1. 1128
  2. 131
  3. 2628
  4. 175
  5. 83
  6. 820
  7. 68
  8. 235
  9. 110
  10. 45
  11. 202
  12. 64
  13. 50
  14. 14
  15. 39
  16. 12
  17. 20th
  18. 25
  19. 900
  20. 78
  21. 99
  22. 79
  23. 144
  24. 135
  25. 17th
  26. 65
  27. 75
  28. 75
  29. 226
  30. 208
  31. 95
  32. 261
  33. 102
  34. 29
  35. 55
  36. 256
  37. 361
  38. 148
  39. 703
  40. 10

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