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Arithmetic Progression Worksheet for Olympiad

Maths Olympiad topic 29: Sequences and AP · Set 360 · 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 14, 16, 18, 20, … is 74? (a) 30th (b) 37th (c) 31st (d) 32nd
  2. 2.What is the 27th term of the AP 17, 22, 27, 32, …? (a) 147 (b) 152 (c) 135 (d) 130
  3. 3.What is the sum of all the whole numbers from 1 to 41? (a) 820 (b) 861 (c) 862 (d) 1722
  4. 4.What is the 23rd term of the AP 2, 4, 6, 8, …? (a) 44 (b) 48 (c) 47 (d) 46
  5. 5.What is the missing term in the AP 13, 20, 27, ?, 41? (a) 33 (b) 35 (c) 41 (d) 34
  6. 6.What is the 14th term of the AP 1, 3, 5, 7, …? (a) 26 (b) 27 (c) 29 (d) 28
  7. 7.What is the sum of all the whole numbers from 1 to 30? (a) 465 (b) 435 (c) 450 (d) 930
  8. 8.What is the sum of the first 5 terms of the AP 1, 2, 3, …? (a) 15 (b) 30 (c) 5 (d) 16
  9. 9.What is the 17th term of the AP 14, 23, 32, 41, …? (a) 144 (b) 167 (c) 153 (d) 158
  10. 10.What is the 12th term of the AP 20, 29, 38, 47, …? (a) 108 (b) 128 (c) 99 (d) 119
  11. 11.Which term of the AP 18, 20, 22, 24, … is 34? (a) 8th (b) 17th (c) 9th (d) 10th
  12. 12.What is the 39th term of the AP 3, 9, 15, 21, …? (a) 234 (b) 237 (c) 231 (d) 228
  13. 13.Which term of the AP 13, 20, 27, 34, … is 160? (a) 24th (b) 22nd (c) 23rd (d) 21st
  14. 14.What is the 11th term of the AP 12, 19, 26, 33, …? (a) 89 (b) 82 (c) 70 (d) 77
  15. 15.What is the 27th term of the AP 16, 24, 32, 40, …? (a) 216 (b) 232 (c) 224 (d) 208
  16. 16.What is the sum of the first 26 odd numbers (1 + 3 + 5 + …)? (a) 676 (b) 702 (c) 51 (d) 351
  17. 17.What is the sum of the first 29 odd numbers (1 + 3 + 5 + …)? (a) 841 (b) 870 (c) 57 (d) 435
  18. 18.What is the sum of all the whole numbers from 1 to 26? (a) 351 (b) 702 (c) 325 (d) 338
  19. 19.What is the sum of the first 7 terms of the AP 8, 9, 10, …? (a) 78 (b) 14 (c) 77 (d) 154
  20. 20.What is the missing term in the AP 13, 16, 19, ?, 25? (a) 21 (b) 23 (c) 25 (d) 22
  21. 21.Which term of the AP 9, 16, 23, 30, … is 149? (a) 23rd (b) 20th (c) 22nd (d) 21st
  22. 22.Which term of the AP 1, 5, 9, 13, … is 61? (a) 18th (b) 17th (c) 16th (d) 15th
  23. 23.What is the sum of all the whole numbers from 1 to 64? (a) 2048 (b) 4160 (c) 2080 (d) 2016
  24. 24.What is the sum of the first 5 terms of the AP 3, 5, 7, …? (a) 70 (b) 40 (c) 35 (d) 11
  25. 25.What is the 29th term of the AP 20, 26, 32, 38, …? (a) 194 (b) 188 (c) 174 (d) 168
  26. 26.What is the 24th term of the AP 10, 19, 28, 37, …? (a) 207 (b) 226 (c) 216 (d) 217
  27. 27.What is the sum of all the whole numbers from 1 to 72? (a) 2628 (b) 2556 (c) 2592 (d) 5256
  28. 28.What is the sum of the first 11 terms of the AP 2, 4, 6, …? (a) 143 (b) 132 (c) 264 (d) 22
  29. 29.What is the sum of the first 22 odd numbers (1 + 3 + 5 + …)? (a) 506 (b) 43 (c) 484 (d) 253
  30. 30.What is the sum of the first 23 odd numbers (1 + 3 + 5 + …)? (a) 276 (b) 45 (c) 529 (d) 552
  31. 31.Which term of the AP 14, 20, 26, 32, … is 158? (a) 26th (b) 27th (c) 25th (d) 24th
  32. 32.What is the sum of all the whole numbers from 1 to 25? (a) 650 (b) 325 (c) 300 (d) 326
  33. 33.What is the sum of the first 7 terms of the AP 7, 12, 17, …? (a) 37 (b) 154 (c) 159 (d) 308
  34. 34.What is the sum of the first 6 terms of the AP 3, 6, 9, …? (a) 18 (b) 72 (c) 126 (d) 63
  35. 35.What is the sum of the first 11 terms of the AP 4, 5, 6, …? (a) 100 (b) 198 (c) 14 (d) 99
  36. 36.What is the sum of the first 5 odd numbers (1 + 3 + 5 + …)? (a) 15 (b) 9 (c) 30 (d) 25
  37. 37.What is the 36th term of the AP 15, 21, 27, 33, …? (a) 231 (b) 210 (c) 216 (d) 225
  38. 38.What is the 30th term of the AP 7, 11, 15, 19, …? (a) 127 (b) 120 (c) 123 (d) 116
  39. 39.What is the sum of the first 7 odd numbers (1 + 3 + 5 + …)? (a) 28 (b) 56 (c) 13 (d) 49
  40. 40.What is the 10th term of the AP 8, 17, 26, 35, …? (a) 81 (b) 98 (c) 90 (d) 89

Answer key

  1. 31st
  2. 147
  3. 861
  4. 46
  5. 34
  6. 27
  7. 465
  8. 15
  9. 158
  10. 119
  11. 9th
  12. 231
  13. 22nd
  14. 82
  15. 224
  16. 676
  17. 841
  18. 351
  19. 77
  20. 22
  21. 21st
  22. 16th
  23. 2080
  24. 35
  25. 188
  26. 217
  27. 2628
  28. 132
  29. 484
  30. 529
  31. 25th
  32. 325
  33. 154
  34. 63
  35. 99
  36. 25
  37. 225
  38. 123
  39. 49
  40. 89

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