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Arithmetic Progression Worksheet for Olympiad

Maths Olympiad topic 29: Sequences and AP · Set 820 · 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.Which term of the AP 5, 11, 17, 23, … is 143? (a) 25th (b) 24th (c) 23rd (d) 26th
  2. 2.What is the sum of all the whole numbers from 1 to 73? (a) 2701 (b) 2702 (c) 2628 (d) 5402
  3. 3.What is the sum of the first 9 terms of the AP 8, 13, 18, …? (a) 257 (b) 48 (c) 252 (d) 504
  4. 4.What is the sum of all the whole numbers from 1 to 19? (a) 190 (b) 380 (c) 191 (d) 171
  5. 5.What is the 13th term of the AP 14, 22, 30, 38, …? (a) 104 (b) 110 (c) 96 (d) 118
  6. 6.What is the sum of the first 6 odd numbers (1 + 3 + 5 + …)? (a) 36 (b) 42 (c) 11 (d) 21
  7. 7.What is the missing term in the AP 20, ?, 34, 41, 48? (a) 34 (b) 28 (c) 26 (d) 27
  8. 8.What is the sum of the first 11 terms of the AP 3, 4, 5, …? (a) 88 (b) 176 (c) 89 (d) 13
  9. 9.What is the missing term in the AP 6, ?, 14, 18, 22? (a) 11 (b) 9 (c) 10 (d) 14
  10. 10.Which term of the AP 9, 17, 25, 33, … is 113? (a) 13th (b) 15th (c) 14th (d) 16th
  11. 11.What is the 26th term of the AP 4, 8, 12, 16, …? (a) 105 (b) 108 (c) 100 (d) 104
  12. 12.What is the 22nd term of the AP 5, 11, 17, 23, …? (a) 126 (b) 132 (c) 137 (d) 131
  13. 13.What is the sum of all the whole numbers from 1 to 97? (a) 4656 (b) 4753 (c) 4754 (d) 9506
  14. 14.What is the 14th term of the AP 12, 19, 26, 33, …? (a) 91 (b) 110 (c) 98 (d) 103
  15. 15.What is the sum of all the whole numbers from 1 to 21? (a) 210 (b) 232 (c) 462 (d) 231
  16. 16.What is the sum of the first 12 odd numbers (1 + 3 + 5 + …)? (a) 23 (b) 78 (c) 144 (d) 156
  17. 17.What is the 34th term of the AP 14, 20, 26, 32, …? (a) 212 (b) 218 (c) 198 (d) 204
  18. 18.What is the 20th term of the AP 3, 11, 19, 27, …? (a) 160 (b) 155 (c) 163 (d) 152
  19. 19.Which term of the AP 19, 26, 33, 40, … is 96? (a) 12th (b) 14th (c) 11th (d) 13th
  20. 20.Which term of the AP 20, 25, 30, 35, … is 210? (a) 42nd (b) 39th (c) 40th (d) 38th
  21. 21.What is the 27th term of the AP 14, 16, 18, 20, …? (a) 54 (b) 52 (c) 68 (d) 66
  22. 22.What is the 23rd term of the AP 9, 15, 21, 27, …? (a) 132 (b) 141 (c) 147 (d) 138
  23. 23.What is the missing term in the AP 4, 9, 14, ?, 24? (a) 19 (b) 20 (c) 18 (d) 24
  24. 24.What is the 15th term of the AP 3, 7, 11, 15, …? (a) 63 (b) 56 (c) 60 (d) 59
  25. 25.What is the 38th term of the AP 3, 5, 7, 9, …? (a) 77 (b) 74 (c) 79 (d) 76
  26. 26.What is the 20th term of the AP 13, 16, 19, 22, …? (a) 57 (b) 60 (c) 73 (d) 70
  27. 27.What is the missing term in the AP 19, 26, 33, ?, 47? (a) 39 (b) 47 (c) 41 (d) 40
  28. 28.What is the 35th term of the AP 20, 22, 24, 26, …? (a) 90 (b) 88 (c) 70 (d) 68
  29. 29.What is the 22nd term of the AP 3, 10, 17, 24, …? (a) 157 (b) 154 (c) 150 (d) 147
  30. 30.What is the 35th term of the AP 2, 4, 6, 8, …? (a) 70 (b) 71 (c) 72 (d) 68
  31. 31.What is the sum of all the whole numbers from 1 to 93? (a) 4371 (b) 4372 (c) 8742 (d) 4278
  32. 32.What is the sum of the first 6 terms of the AP 7, 9, 11, …? (a) 144 (b) 72 (c) 17 (d) 78
  33. 33.What is the 17th term of the AP 10, 12, 14, 16, …? (a) 42 (b) 34 (c) 32 (d) 44
  34. 34.What is the sum of the first 7 terms of the AP 3, 4, 5, …? (a) 42 (b) 84 (c) 9 (d) 43
  35. 35.What is the sum of the first 22 odd numbers (1 + 3 + 5 + …)? (a) 43 (b) 484 (c) 506 (d) 253
  36. 36.What is the sum of the first 11 terms of the AP 4, 5, 6, …? (a) 99 (b) 14 (c) 100 (d) 198
  37. 37.Which term of the AP 13, 20, 27, 34, … is 181? (a) 26th (b) 24th (c) 27th (d) 25th
  38. 38.Which term of the AP 1, 3, 5, 7, … is 55? (a) 30th (b) 27th (c) 28th (d) 29th
  39. 39.What is the missing term in the AP 7, 10, ?, 16, 19? (a) 14 (b) 12 (c) 16 (d) 13
  40. 40.What is the sum of all the whole numbers from 1 to 53? (a) 1431 (b) 2862 (c) 1378 (d) 1432

Answer key

  1. 24th
  2. 2701
  3. 252
  4. 190
  5. 110
  6. 36
  7. 27
  8. 88
  9. 10
  10. 14th
  11. 104
  12. 131
  13. 4753
  14. 103
  15. 231
  16. 144
  17. 212
  18. 155
  19. 12th
  20. 39th
  21. 66
  22. 141
  23. 19
  24. 59
  25. 77
  26. 70
  27. 40
  28. 88
  29. 150
  30. 70
  31. 4371
  32. 72
  33. 42
  34. 42
  35. 484
  36. 99
  37. 25th
  38. 28th
  39. 13
  40. 1431

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