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Arithmetic Progression Worksheet for Olympiad

Maths Olympiad topic 29: Sequences and AP · Set 328 · 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 15th term of the AP 7, 13, 19, 25, …? (a) 97 (b) 84 (c) 90 (d) 91
  2. 2.Which term of the AP 18, 20, 22, 24, … is 50? (a) 18th (b) 17th (c) 25th (d) 16th
  3. 3.What is the 20th term of the AP 8, 12, 16, 20, …? (a) 80 (b) 76 (c) 88 (d) 84
  4. 4.What is the 18th term of the AP 14, 17, 20, 23, …? (a) 51 (b) 68 (c) 65 (d) 54
  5. 5.What is the sum of the first 18 odd numbers (1 + 3 + 5 + …)? (a) 171 (b) 342 (c) 324 (d) 35
  6. 6.What is the sum of the first 10 terms of the AP 4, 6, 8, …? (a) 22 (b) 140 (c) 260 (d) 130
  7. 7.Which term of the AP 7, 14, 21, 28, … is 119? (a) 18th (b) 16th (c) 17th (d) 19th
  8. 8.What is the 19th term of the AP 10, 13, 16, 19, …? (a) 54 (b) 57 (c) 64 (d) 67
  9. 9.What is the sum of the first 12 terms of the AP 2, 7, 12, …? (a) 708 (b) 354 (c) 384 (d) 57
  10. 10.What is the sum of the first 9 terms of the AP 10, 14, 18, …? (a) 42 (b) 468 (c) 252 (d) 234
  11. 11.What is the 28th term of the AP 12, 20, 28, 36, …? (a) 228 (b) 216 (c) 236 (d) 224
  12. 12.What is the missing term in the AP 7, 10, ?, 16, 19? (a) 13 (b) 16 (c) 12 (d) 14
  13. 13.What is the sum of the first 10 terms of the AP 3, 9, 15, …? (a) 57 (b) 300 (c) 330 (d) 600
  14. 14.Which term of the AP 12, 16, 20, 24, … is 96? (a) 22nd (b) 21st (c) 23rd (d) 24th
  15. 15.What is the missing term in the AP 8, 10, 12, ?, 16? (a) 14 (b) 16 (c) 13 (d) 15
  16. 16.What is the sum of the first 7 terms of the AP 9, 13, 17, …? (a) 294 (b) 33 (c) 147 (d) 161
  17. 17.Which term of the AP 14, 18, 22, 26, … is 130? (a) 30th (b) 32nd (c) 31st (d) 29th
  18. 18.Which term of the AP 5, 10, 15, 20, … is 50? (a) 10th (b) 12th (c) 11th (d) 9th
  19. 19.What is the sum of the first 6 terms of the AP 3, 7, 11, …? (a) 156 (b) 78 (c) 90 (d) 23
  20. 20.What is the sum of the first 9 terms of the AP 7, 13, 19, …? (a) 558 (b) 306 (c) 279 (d) 55
  21. 21.What is the 17th term of the AP 1, 6, 11, 16, …? (a) 86 (b) 85 (c) 81 (d) 80
  22. 22.Which term of the AP 16, 25, 34, 43, … is 151? (a) 15th (b) 16th (c) 17th (d) 18th
  23. 23.What is the sum of the first 22 odd numbers (1 + 3 + 5 + …)? (a) 253 (b) 484 (c) 43 (d) 506
  24. 24.What is the sum of all the whole numbers from 1 to 23? (a) 552 (b) 276 (c) 253 (d) 277
  25. 25.What is the 29th term of the AP 5, 13, 21, 29, …? (a) 232 (b) 224 (c) 229 (d) 237
  26. 26.What is the missing term in the AP 11, ?, 21, 26, 31? (a) 17 (b) 15 (c) 21 (d) 16
  27. 27.What is the sum of the first 12 terms of the AP 5, 6, 7, …? (a) 132 (b) 16 (c) 126 (d) 252
  28. 28.What is the 22nd term of the AP 20, 24, 28, 32, …? (a) 108 (b) 104 (c) 88 (d) 84
  29. 29.What is the 14th term of the AP 17, 23, 29, 35, …? (a) 101 (b) 95 (c) 84 (d) 78
  30. 30.What is the sum of the first 5 terms of the AP 10, 15, 20, …? (a) 105 (b) 30 (c) 100 (d) 200
  31. 31.What is the 10th term of the AP 15, 18, 21, 24, …? (a) 45 (b) 27 (c) 42 (d) 30
  32. 32.What is the sum of the first 6 terms of the AP 5, 11, 17, …? (a) 35 (b) 138 (c) 120 (d) 240
  33. 33.What is the sum of the first 5 terms of the AP 6, 11, 16, …? (a) 26 (b) 160 (c) 85 (d) 80
  34. 34.What is the sum of the first 24 odd numbers (1 + 3 + 5 + …)? (a) 300 (b) 576 (c) 47 (d) 600
  35. 35.What is the sum of all the whole numbers from 1 to 19? (a) 191 (b) 171 (c) 380 (d) 190
  36. 36.What is the sum of the first 6 terms of the AP 1, 6, 11, …? (a) 81 (b) 96 (c) 162 (d) 26
  37. 37.What is the 22nd term of the AP 3, 11, 19, 27, …? (a) 171 (b) 168 (c) 179 (d) 176
  38. 38.What is the sum of the first 9 terms of the AP 3, 7, 11, …? (a) 35 (b) 342 (c) 171 (d) 189
  39. 39.What is the sum of the first 5 terms of the AP 2, 3, 4, …? (a) 21 (b) 20 (c) 40 (d) 6
  40. 40.What is the sum of all the whole numbers from 1 to 47? (a) 1081 (b) 2256 (c) 1128 (d) 1129

Answer key

  1. 91
  2. 17th
  3. 84
  4. 65
  5. 324
  6. 130
  7. 17th
  8. 64
  9. 354
  10. 234
  11. 228
  12. 13
  13. 300
  14. 22nd
  15. 14
  16. 147
  17. 30th
  18. 10th
  19. 78
  20. 279
  21. 81
  22. 16th
  23. 484
  24. 276
  25. 229
  26. 16
  27. 126
  28. 104
  29. 95
  30. 100
  31. 42
  32. 120
  33. 80
  34. 576
  35. 190
  36. 81
  37. 171
  38. 171
  39. 20
  40. 1128

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