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Arithmetic Progression Worksheet for Olympiad

Maths Olympiad topic 29: Sequences and AP · Set 435 · 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 7 odd numbers (1 + 3 + 5 + …)? (a) 56 (b) 49 (c) 13 (d) 28
  2. 2.What is the 26th term of the AP 9, 13, 17, 21, …? (a) 100 (b) 113 (c) 104 (d) 109
  3. 3.What is the missing term in the AP 6, ?, 24, 33, 42? (a) 15 (b) 14 (c) 16 (d) 24
  4. 4.What is the sum of the first 8 terms of the AP 9, 10, 11, …? (a) 16 (b) 104 (c) 200 (d) 100
  5. 5.What is the sum of the first 11 terms of the AP 10, 15, 20, …? (a) 60 (b) 390 (c) 385 (d) 770
  6. 6.What is the sum of the first 7 terms of the AP 10, 12, 14, …? (a) 224 (b) 119 (c) 112 (d) 22
  7. 7.What is the sum of the first 11 terms of the AP 8, 14, 20, …? (a) 418 (b) 68 (c) 836 (d) 451
  8. 8.What is the sum of the first 23 odd numbers (1 + 3 + 5 + …)? (a) 552 (b) 529 (c) 45 (d) 276
  9. 9.What is the sum of the first 18 odd numbers (1 + 3 + 5 + …)? (a) 35 (b) 342 (c) 324 (d) 171
  10. 10.What is the sum of the first 12 terms of the AP 2, 6, 10, …? (a) 288 (b) 312 (c) 576 (d) 46
  11. 11.What is the sum of the first 12 terms of the AP 3, 9, 15, …? (a) 468 (b) 432 (c) 864 (d) 69
  12. 12.What is the sum of the first 8 terms of the AP 8, 11, 14, …? (a) 148 (b) 29 (c) 296 (d) 160
  13. 13.What is the 28th term of the AP 2, 10, 18, 26, …? (a) 216 (b) 226 (c) 218 (d) 224
  14. 14.What is the missing term in the AP 4, 8, ?, 16, 20? (a) 16 (b) 13 (c) 11 (d) 12
  15. 15.What is the 15th term of the AP 18, 22, 26, 30, …? (a) 78 (b) 56 (c) 60 (d) 74
  16. 16.What is the sum of all the whole numbers from 1 to 72? (a) 5256 (b) 2592 (c) 2556 (d) 2628
  17. 17.Which term of the AP 14, 19, 24, 29, … is 89? (a) 17th (b) 18th (c) 16th (d) 15th
  18. 18.What is the sum of all the whole numbers from 1 to 46? (a) 1081 (b) 1035 (c) 1058 (d) 2162
  19. 19.Which term of the AP 1, 10, 19, 28, … is 73? (a) 10th (b) 11th (c) 9th (d) 8th
  20. 20.What is the 29th term of the AP 2, 5, 8, 11, …? (a) 89 (b) 87 (c) 86 (d) 84
  21. 21.What is the missing term in the AP 2, 6, 10, ?, 18? (a) 18 (b) 15 (c) 13 (d) 14
  22. 22.What is the 13th term of the AP 1, 5, 9, 13, …? (a) 48 (b) 52 (c) 49 (d) 53
  23. 23.What is the missing term in the AP 9, ?, 13, 15, 17? (a) 12 (b) 13 (c) 11 (d) 10
  24. 24.What is the 30th term of the AP 1, 8, 15, 22, …? (a) 211 (b) 203 (c) 210 (d) 204
  25. 25.What is the sum of the first 11 terms of the AP 3, 5, 7, …? (a) 286 (b) 23 (c) 154 (d) 143
  26. 26.What is the 15th term of the AP 5, 10, 15, 20, …? (a) 75 (b) 76 (c) 70 (d) 80
  27. 27.Which term of the AP 3, 9, 15, 21, … is 219? (a) 38th (b) 36th (c) 37th (d) 39th
  28. 28.Which term of the AP 18, 24, 30, 36, … is 144? (a) 24th (b) 22nd (c) 21st (d) 23rd
  29. 29.What is the missing term in the AP 9, 12, 15, ?, 21? (a) 18 (b) 21 (c) 17 (d) 19
  30. 30.What is the sum of the first 5 terms of the AP 9, 13, 17, …? (a) 25 (b) 170 (c) 95 (d) 85
  31. 31.What is the 39th term of the AP 8, 13, 18, 23, …? (a) 198 (b) 195 (c) 190 (d) 203
  32. 32.What is the sum of all the whole numbers from 1 to 30? (a) 930 (b) 435 (c) 465 (d) 450
  33. 33.What is the sum of the first 6 terms of the AP 1, 3, 5, …? (a) 42 (b) 72 (c) 11 (d) 36
  34. 34.What is the sum of the first 7 terms of the AP 7, 11, 15, …? (a) 266 (b) 147 (c) 31 (d) 133
  35. 35.What is the sum of the first 10 terms of the AP 8, 10, 12, …? (a) 26 (b) 180 (c) 170 (d) 340
  36. 36.What is the sum of all the whole numbers from 1 to 91? (a) 4187 (b) 8372 (c) 4186 (d) 4095
  37. 37.What is the sum of the first 12 terms of the AP 6, 12, 18, …? (a) 936 (b) 504 (c) 72 (d) 468
  38. 38.What is the sum of the first 10 terms of the AP 8, 11, 14, …? (a) 430 (b) 215 (c) 35 (d) 230
  39. 39.What is the sum of the first 19 odd numbers (1 + 3 + 5 + …)? (a) 361 (b) 37 (c) 380 (d) 190
  40. 40.What is the 39th term of the AP 8, 11, 14, 17, …? (a) 122 (b) 114 (c) 117 (d) 125

Answer key

  1. 49
  2. 109
  3. 15
  4. 100
  5. 385
  6. 112
  7. 418
  8. 529
  9. 324
  10. 288
  11. 432
  12. 148
  13. 218
  14. 12
  15. 74
  16. 2628
  17. 16th
  18. 1081
  19. 9th
  20. 86
  21. 14
  22. 49
  23. 11
  24. 204
  25. 143
  26. 75
  27. 37th
  28. 22nd
  29. 18
  30. 85
  31. 198
  32. 465
  33. 36
  34. 133
  35. 170
  36. 4186
  37. 468
  38. 215
  39. 361
  40. 122

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