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Arithmetic Progression Worksheet for Olympiad

Maths Olympiad topic 29: Sequences and AP · Set 625 · 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 terms of the AP 8, 10, 12, …? (a) 105 (b) 196 (c) 20 (d) 98
  2. 2.What is the sum of all the whole numbers from 1 to 23? (a) 253 (b) 277 (c) 552 (d) 276
  3. 3.What is the sum of the first 9 odd numbers (1 + 3 + 5 + …)? (a) 90 (b) 17 (c) 45 (d) 81
  4. 4.What is the sum of all the whole numbers from 1 to 39? (a) 741 (b) 781 (c) 1560 (d) 780
  5. 5.What is the sum of the first 26 odd numbers (1 + 3 + 5 + …)? (a) 51 (b) 702 (c) 676 (d) 351
  6. 6.What is the 32nd term of the AP 5, 7, 9, 11, …? (a) 69 (b) 62 (c) 67 (d) 64
  7. 7.What is the 30th term of the AP 15, 18, 21, 24, …? (a) 105 (b) 87 (c) 102 (d) 90
  8. 8.What is the missing term in the AP 17, 24, ?, 38, 45? (a) 30 (b) 38 (c) 31 (d) 32
  9. 9.What is the sum of the first 9 terms of the AP 6, 9, 12, …? (a) 30 (b) 165 (c) 162 (d) 324
  10. 10.What is the missing term in the AP 6, 14, 22, ?, 38? (a) 38 (b) 30 (c) 29 (d) 31
  11. 11.What is the missing term in the AP 15, 20, ?, 30, 35? (a) 30 (b) 26 (c) 24 (d) 25
  12. 12.What is the 37th term of the AP 20, 27, 34, 41, …? (a) 279 (b) 252 (c) 272 (d) 259
  13. 13.What is the sum of the first 24 odd numbers (1 + 3 + 5 + …)? (a) 47 (b) 600 (c) 576 (d) 300
  14. 14.Which term of the AP 3, 6, 9, 12, … is 42? (a) 15th (b) 16th (c) 14th (d) 13th
  15. 15.What is the missing term in the AP 4, 9, 14, ?, 24? (a) 20 (b) 18 (c) 24 (d) 19
  16. 16.What is the missing term in the AP 15, 18, ?, 24, 27? (a) 24 (b) 21 (c) 22 (d) 20
  17. 17.What is the sum of the first 8 terms of the AP 2, 4, 6, …? (a) 72 (b) 80 (c) 144 (d) 16
  18. 18.What is the 16th term of the AP 13, 17, 21, 25, …? (a) 60 (b) 77 (c) 73 (d) 64
  19. 19.What is the sum of the first 6 terms of the AP 2, 7, 12, …? (a) 102 (b) 27 (c) 87 (d) 174
  20. 20.Which term of the AP 3, 6, 9, 12, … is 27? (a) 10th (b) 9th (c) 11th (d) 8th
  21. 21.What is the sum of the first 9 terms of the AP 5, 9, 13, …? (a) 378 (b) 37 (c) 189 (d) 207
  22. 22.Which term of the AP 15, 22, 29, 36, … is 190? (a) 25th (b) 27th (c) 26th (d) 28th
  23. 23.What is the 31st term of the AP 6, 14, 22, 30, …? (a) 246 (b) 240 (c) 254 (d) 248
  24. 24.What is the 11th term of the AP 7, 10, 13, 16, …? (a) 33 (b) 40 (c) 37 (d) 30
  25. 25.What is the sum of all the whole numbers from 1 to 46? (a) 1035 (b) 1058 (c) 1081 (d) 2162
  26. 26.What is the sum of all the whole numbers from 1 to 74? (a) 5550 (b) 2738 (c) 2775 (d) 2701
  27. 27.What is the missing term in the AP 2, 6, ?, 14, 18? (a) 10 (b) 11 (c) 14 (d) 9
  28. 28.What is the 35th term of the AP 2, 5, 8, 11, …? (a) 107 (b) 105 (c) 104 (d) 102
  29. 29.What is the sum of the first 22 odd numbers (1 + 3 + 5 + …)? (a) 506 (b) 253 (c) 484 (d) 43
  30. 30.What is the 30th term of the AP 6, 11, 16, 21, …? (a) 150 (b) 156 (c) 151 (d) 145
  31. 31.What is the sum of the first 14 odd numbers (1 + 3 + 5 + …)? (a) 105 (b) 196 (c) 27 (d) 210
  32. 32.What is the sum of the first 5 terms of the AP 7, 10, 13, …? (a) 19 (b) 68 (c) 130 (d) 65
  33. 33.What is the sum of all the whole numbers from 1 to 57? (a) 1596 (b) 3306 (c) 1653 (d) 1654
  34. 34.What is the sum of the first 7 terms of the AP 9, 10, 11, …? (a) 15 (b) 168 (c) 84 (d) 85
  35. 35.What is the missing term in the AP 7, 16, 25, ?, 43? (a) 33 (b) 43 (c) 34 (d) 35
  36. 36.What is the 13th term of the AP 8, 14, 20, 26, …? (a) 78 (b) 72 (c) 86 (d) 80
  37. 37.What is the sum of the first 29 odd numbers (1 + 3 + 5 + …)? (a) 435 (b) 870 (c) 57 (d) 841
  38. 38.What is the 34th term of the AP 6, 14, 22, 30, …? (a) 270 (b) 278 (c) 264 (d) 272
  39. 39.What is the 10th term of the AP 12, 15, 18, 21, …? (a) 30 (b) 42 (c) 27 (d) 39
  40. 40.What is the sum of the first 6 terms of the AP 2, 3, 4, …? (a) 30 (b) 7 (c) 27 (d) 54

Answer key

  1. 98
  2. 276
  3. 81
  4. 780
  5. 676
  6. 67
  7. 102
  8. 31
  9. 162
  10. 30
  11. 25
  12. 272
  13. 576
  14. 14th
  15. 19
  16. 21
  17. 72
  18. 73
  19. 87
  20. 9th
  21. 189
  22. 26th
  23. 246
  24. 37
  25. 1081
  26. 2775
  27. 10
  28. 104
  29. 484
  30. 151
  31. 196
  32. 65
  33. 1653
  34. 84
  35. 34
  36. 80
  37. 841
  38. 270
  39. 39
  40. 27

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