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Arithmetic Progression Worksheet for Olympiad

Maths Olympiad topic 29: Sequences and AP · Set 795 · 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 28 odd numbers (1 + 3 + 5 + …)? (a) 812 (b) 55 (c) 784 (d) 406
  2. 2.What is the sum of the first 8 odd numbers (1 + 3 + 5 + …)? (a) 36 (b) 72 (c) 64 (d) 15
  3. 3.What is the sum of the first 7 terms of the AP 6, 11, 16, …? (a) 36 (b) 147 (c) 294 (d) 152
  4. 4.What is the sum of the first 9 terms of the AP 8, 9, 10, …? (a) 108 (b) 16 (c) 216 (d) 109
  5. 5.What is the 26th term of the AP 4, 11, 18, 25, …? (a) 182 (b) 186 (c) 175 (d) 179
  6. 6.Which term of the AP 15, 24, 33, 42, … is 249? (a) 29th (b) 28th (c) 26th (d) 27th
  7. 7.Which term of the AP 4, 8, 12, 16, … is 160? (a) 39th (b) 40th (c) 41st (d) 42nd
  8. 8.What is the sum of the first 20 odd numbers (1 + 3 + 5 + …)? (a) 210 (b) 39 (c) 400 (d) 420
  9. 9.What is the missing term in the AP 9, ?, 23, 30, 37? (a) 15 (b) 23 (c) 16 (d) 17
  10. 10.What is the sum of all the whole numbers from 1 to 73? (a) 2628 (b) 5402 (c) 2701 (d) 2702
  11. 11.What is the sum of the first 7 terms of the AP 7, 9, 11, …? (a) 182 (b) 98 (c) 91 (d) 19
  12. 12.Which term of the AP 6, 9, 12, 15, … is 39? (a) 14th (b) 12th (c) 13th (d) 11th
  13. 13.What is the 38th term of the AP 8, 16, 24, 32, …? (a) 296 (b) 304 (c) 305 (d) 312
  14. 14.What is the sum of the first 6 terms of the AP 2, 6, 10, …? (a) 144 (b) 84 (c) 22 (d) 72
  15. 15.What is the sum of the first 11 terms of the AP 8, 14, 20, …? (a) 451 (b) 418 (c) 68 (d) 836
  16. 16.What is the sum of the first 6 terms of the AP 1, 7, 13, …? (a) 114 (b) 31 (c) 96 (d) 192
  17. 17.What is the 11th term of the AP 6, 10, 14, 18, …? (a) 44 (b) 40 (c) 46 (d) 50
  18. 18.What is the sum of the first 5 terms of the AP 4, 9, 14, …? (a) 75 (b) 24 (c) 70 (d) 140
  19. 19.What is the 24th term of the AP 9, 18, 27, 36, …? (a) 217 (b) 207 (c) 216 (d) 225
  20. 20.What is the missing term in the AP 11, 19, 27, ?, 43? (a) 36 (b) 35 (c) 34 (d) 43
  21. 21.What is the sum of the first 19 odd numbers (1 + 3 + 5 + …)? (a) 380 (b) 37 (c) 361 (d) 190
  22. 22.What is the sum of the first 6 odd numbers (1 + 3 + 5 + …)? (a) 36 (b) 42 (c) 21 (d) 11
  23. 23.What is the sum of all the whole numbers from 1 to 54? (a) 1431 (b) 2970 (c) 1458 (d) 1485
  24. 24.What is the sum of the first 5 terms of the AP 6, 12, 18, …? (a) 180 (b) 105 (c) 30 (d) 90
  25. 25.What is the sum of the first 8 terms of the AP 6, 9, 12, …? (a) 144 (b) 132 (c) 264 (d) 27
  26. 26.What is the missing term in the AP 15, 18, ?, 24, 27? (a) 21 (b) 24 (c) 20 (d) 22
  27. 27.Which term of the AP 5, 10, 15, 20, … is 45? (a) 11th (b) 8th (c) 10th (d) 9th
  28. 28.What is the sum of the first 7 terms of the AP 9, 13, 17, …? (a) 294 (b) 147 (c) 161 (d) 33
  29. 29.Which term of the AP 15, 23, 31, 39, … is 207? (a) 24th (b) 25th (c) 26th (d) 27th
  30. 30.What is the sum of the first 6 terms of the AP 9, 13, 17, …? (a) 29 (b) 126 (c) 114 (d) 228
  31. 31.What is the sum of the first 5 terms of the AP 2, 6, 10, …? (a) 100 (b) 50 (c) 18 (d) 60
  32. 32.What is the sum of the first 23 odd numbers (1 + 3 + 5 + …)? (a) 552 (b) 45 (c) 276 (d) 529
  33. 33.Which term of the AP 16, 21, 26, 31, … is 171? (a) 33rd (b) 34th (c) 31st (d) 32nd
  34. 34.What is the missing term in the AP 17, ?, 33, 41, 49? (a) 33 (b) 25 (c) 26 (d) 24
  35. 35.What is the sum of all the whole numbers from 1 to 95? (a) 4561 (b) 9120 (c) 4560 (d) 4465
  36. 36.What is the 14th term of the AP 6, 9, 12, 15, …? (a) 42 (b) 48 (c) 45 (d) 39
  37. 37.What is the missing term in the AP 16, 24, 32, ?, 48? (a) 41 (b) 48 (c) 39 (d) 40
  38. 38.What is the 38th term of the AP 11, 20, 29, 38, …? (a) 342 (b) 353 (c) 333 (d) 344
  39. 39.What is the missing term in the AP 14, 19, ?, 29, 34? (a) 25 (b) 29 (c) 24 (d) 23
  40. 40.Which term of the AP 3, 11, 19, 27, … is 307? (a) 41st (b) 39th (c) 38th (d) 40th

Answer key

  1. 784
  2. 64
  3. 147
  4. 108
  5. 179
  6. 27th
  7. 40th
  8. 400
  9. 16
  10. 2701
  11. 91
  12. 12th
  13. 304
  14. 72
  15. 418
  16. 96
  17. 46
  18. 70
  19. 216
  20. 35
  21. 361
  22. 36
  23. 1485
  24. 90
  25. 132
  26. 21
  27. 9th
  28. 147
  29. 25th
  30. 114
  31. 50
  32. 529
  33. 32nd
  34. 25
  35. 4560
  36. 45
  37. 40
  38. 344
  39. 24
  40. 39th

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