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Arithmetic Progression Worksheet for Olympiad

Maths Olympiad topic 29: Sequences and AP · Set 498 · 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 missing term in the AP 3, ?, 21, 30, 39? (a) 11 (b) 21 (c) 13 (d) 12
  2. 2.Which term of the AP 11, 19, 27, 35, … is 75? (a) 11th (b) 9th (c) 10th (d) 8th
  3. 3.Which term of the AP 10, 19, 28, 37, … is 352? (a) 38th (b) 41st (c) 40th (d) 39th
  4. 4.What is the 27th term of the AP 2, 4, 6, 8, …? (a) 54 (b) 52 (c) 55 (d) 56
  5. 5.What is the missing term in the AP 8, 13, ?, 23, 28? (a) 17 (b) 19 (c) 18 (d) 23
  6. 6.What is the 19th term of the AP 8, 11, 14, 17, …? (a) 54 (b) 65 (c) 62 (d) 57
  7. 7.What is the sum of all the whole numbers from 1 to 74? (a) 2775 (b) 2701 (c) 2738 (d) 5550
  8. 8.What is the sum of all the whole numbers from 1 to 94? (a) 4418 (b) 8930 (c) 4465 (d) 4371
  9. 9.What is the 24th term of the AP 13, 17, 21, 25, …? (a) 92 (b) 96 (c) 109 (d) 105
  10. 10.What is the sum of the first 5 terms of the AP 6, 7, 8, …? (a) 41 (b) 10 (c) 80 (d) 40
  11. 11.What is the missing term in the AP 8, 13, 18, ?, 28? (a) 23 (b) 22 (c) 28 (d) 24
  12. 12.What is the sum of the first 11 odd numbers (1 + 3 + 5 + …)? (a) 21 (b) 121 (c) 66 (d) 132
  13. 13.What is the sum of the first 7 terms of the AP 9, 11, 13, …? (a) 112 (b) 210 (c) 105 (d) 21
  14. 14.What is the 12th term of the AP 1, 10, 19, 28, …? (a) 100 (b) 109 (c) 99 (d) 108
  15. 15.What is the sum of the first 5 terms of the AP 1, 6, 11, …? (a) 60 (b) 110 (c) 55 (d) 21
  16. 16.Which term of the AP 6, 10, 14, 18, … is 98? (a) 23rd (b) 25th (c) 24th (d) 26th
  17. 17.What is the 25th term of the AP 7, 9, 11, 13, …? (a) 48 (b) 57 (c) 55 (d) 50
  18. 18.What is the sum of all the whole numbers from 1 to 39? (a) 741 (b) 1560 (c) 781 (d) 780
  19. 19.What is the 36th term of the AP 8, 17, 26, 35, …? (a) 324 (b) 332 (c) 315 (d) 323
  20. 20.What is the missing term in the AP 11, 14, 17, ?, 23? (a) 19 (b) 20 (c) 21 (d) 23
  21. 21.What is the 12th term of the AP 14, 16, 18, 20, …? (a) 22 (b) 24 (c) 38 (d) 36
  22. 22.What is the sum of the first 8 terms of the AP 2, 4, 6, …? (a) 80 (b) 16 (c) 144 (d) 72
  23. 23.What is the 39th term of the AP 19, 21, 23, 25, …? (a) 78 (b) 97 (c) 76 (d) 95
  24. 24.What is the sum of the first 23 odd numbers (1 + 3 + 5 + …)? (a) 529 (b) 276 (c) 45 (d) 552
  25. 25.What is the sum of all the whole numbers from 1 to 71? (a) 2556 (b) 5112 (c) 2485 (d) 2557
  26. 26.What is the sum of the first 5 terms of the AP 3, 7, 11, …? (a) 65 (b) 19 (c) 110 (d) 55
  27. 27.What is the sum of the first 15 odd numbers (1 + 3 + 5 + …)? (a) 240 (b) 225 (c) 120 (d) 29
  28. 28.What is the sum of the first 5 terms of the AP 4, 6, 8, …? (a) 80 (b) 45 (c) 12 (d) 40
  29. 29.Which term of the AP 13, 22, 31, 40, … is 310? (a) 36th (b) 34th (c) 33rd (d) 35th
  30. 30.What is the 25th term of the AP 14, 18, 22, 26, …? (a) 96 (b) 100 (c) 114 (d) 110
  31. 31.What is the missing term in the AP 1, 4, ?, 10, 13? (a) 7 (b) 8 (c) 10 (d) 6
  32. 32.What is the missing term in the AP 6, 8, ?, 12, 14? (a) 11 (b) 10 (c) 12 (d) 9
  33. 33.What is the sum of the first 12 terms of the AP 8, 9, 10, …? (a) 19 (b) 162 (c) 168 (d) 324
  34. 34.What is the sum of the first 7 terms of the AP 4, 9, 14, …? (a) 266 (b) 138 (c) 133 (d) 34
  35. 35.What is the 26th term of the AP 8, 10, 12, 14, …? (a) 50 (b) 58 (c) 52 (d) 60
  36. 36.Which term of the AP 12, 21, 30, 39, … is 84? (a) 10th (b) 9th (c) 8th (d) 11th
  37. 37.What is the sum of the first 8 terms of the AP 4, 5, 6, …? (a) 64 (b) 11 (c) 120 (d) 60
  38. 38.What is the sum of the first 9 terms of the AP 7, 12, 17, …? (a) 486 (b) 243 (c) 248 (d) 47
  39. 39.What is the sum of all the whole numbers from 1 to 67? (a) 2278 (b) 2211 (c) 2279 (d) 4556
  40. 40.What is the missing term in the AP 16, 24, 32, ?, 48? (a) 41 (b) 40 (c) 48 (d) 39

Answer key

  1. 12
  2. 9th
  3. 39th
  4. 54
  5. 18
  6. 62
  7. 2775
  8. 4465
  9. 105
  10. 40
  11. 23
  12. 121
  13. 105
  14. 100
  15. 55
  16. 24th
  17. 55
  18. 780
  19. 323
  20. 20
  21. 36
  22. 72
  23. 95
  24. 529
  25. 2556
  26. 55
  27. 225
  28. 40
  29. 34th
  30. 110
  31. 7
  32. 10
  33. 162
  34. 133
  35. 58
  36. 9th
  37. 60
  38. 243
  39. 2278
  40. 40

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