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Arithmetic Progression Worksheet for Olympiad

Maths Olympiad topic 29: Sequences and AP · Set 835 · 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 13, 20, 27, 34, … is 62? (a) 8th (b) 10th (c) 9th (d) 7th
  2. 2.What is the 18th term of the AP 5, 12, 19, 26, …? (a) 119 (b) 126 (c) 124 (d) 131
  3. 3.What is the sum of the first 5 terms of the AP 9, 11, 13, …? (a) 17 (b) 130 (c) 70 (d) 65
  4. 4.What is the missing term in the AP 14, 18, 22, ?, 30? (a) 27 (b) 25 (c) 26 (d) 30
  5. 5.What is the sum of all the whole numbers from 1 to 11? (a) 67 (b) 132 (c) 55 (d) 66
  6. 6.What is the sum of all the whole numbers from 1 to 95? (a) 4560 (b) 4561 (c) 9120 (d) 4465
  7. 7.What is the sum of the first 9 odd numbers (1 + 3 + 5 + …)? (a) 45 (b) 90 (c) 17 (d) 81
  8. 8.What is the sum of the first 20 odd numbers (1 + 3 + 5 + …)? (a) 400 (b) 39 (c) 420 (d) 210
  9. 9.What is the sum of the first 16 odd numbers (1 + 3 + 5 + …)? (a) 272 (b) 31 (c) 256 (d) 136
  10. 10.Which term of the AP 1, 8, 15, 22, … is 113? (a) 19th (b) 16th (c) 18th (d) 17th
  11. 11.What is the sum of the first 7 terms of the AP 1, 2, 3, …? (a) 28 (b) 7 (c) 56 (d) 29
  12. 12.What is the sum of the first 12 terms of the AP 4, 6, 8, …? (a) 360 (b) 180 (c) 192 (d) 26
  13. 13.What is the 12th term of the AP 1, 7, 13, 19, …? (a) 66 (b) 73 (c) 72 (d) 67
  14. 14.What is the sum of all the whole numbers from 1 to 48? (a) 2352 (b) 1176 (c) 1152 (d) 1128
  15. 15.Which term of the AP 5, 9, 13, 17, … is 101? (a) 24th (b) 27th (c) 26th (d) 25th
  16. 16.What is the sum of all the whole numbers from 1 to 67? (a) 2211 (b) 4556 (c) 2279 (d) 2278
  17. 17.What is the sum of the first 5 terms of the AP 1, 7, 13, …? (a) 80 (b) 25 (c) 65 (d) 130
  18. 18.What is the 26th term of the AP 9, 13, 17, 21, …? (a) 109 (b) 104 (c) 113 (d) 100
  19. 19.What is the sum of the first 26 odd numbers (1 + 3 + 5 + …)? (a) 51 (b) 702 (c) 351 (d) 676
  20. 20.Which term of the AP 3, 6, 9, 12, … is 99? (a) 32nd (b) 34th (c) 33rd (d) 35th
  21. 21.What is the missing term in the AP 12, ?, 18, 21, 24? (a) 16 (b) 15 (c) 18 (d) 14
  22. 22.Which term of the AP 12, 15, 18, 21, … is 93? (a) 27th (b) 29th (c) 31st (d) 28th
  23. 23.What is the 28th term of the AP 13, 20, 27, 34, …? (a) 196 (b) 189 (c) 202 (d) 209
  24. 24.What is the missing term in the AP 6, 8, 10, ?, 14? (a) 14 (b) 11 (c) 12 (d) 13
  25. 25.What is the sum of all the whole numbers from 1 to 38? (a) 722 (b) 1482 (c) 741 (d) 703
  26. 26.What is the 25th term of the AP 18, 24, 30, 36, …? (a) 168 (b) 144 (c) 162 (d) 150
  27. 27.What is the sum of the first 10 terms of the AP 6, 8, 10, …? (a) 150 (b) 300 (c) 24 (d) 160
  28. 28.What is the sum of the first 12 terms of the AP 2, 3, 4, …? (a) 13 (b) 90 (c) 180 (d) 96
  29. 29.What is the sum of the first 11 terms of the AP 2, 8, 14, …? (a) 62 (b) 704 (c) 385 (d) 352
  30. 30.What is the sum of the first 9 terms of the AP 9, 15, 21, …? (a) 57 (b) 324 (c) 594 (d) 297
  31. 31.What is the 40th term of the AP 6, 9, 12, 15, …? (a) 126 (b) 117 (c) 120 (d) 123
  32. 32.What is the sum of the first 7 terms of the AP 8, 11, 14, …? (a) 119 (b) 26 (c) 122 (d) 238
  33. 33.What is the sum of the first 29 odd numbers (1 + 3 + 5 + …)? (a) 57 (b) 841 (c) 870 (d) 435
  34. 34.What is the 19th term of the AP 7, 12, 17, 22, …? (a) 90 (b) 95 (c) 102 (d) 97
  35. 35.What is the sum of the first 25 odd numbers (1 + 3 + 5 + …)? (a) 325 (b) 625 (c) 49 (d) 650
  36. 36.What is the sum of all the whole numbers from 1 to 17? (a) 306 (b) 153 (c) 154 (d) 136
  37. 37.What is the sum of the first 9 terms of the AP 8, 13, 18, …? (a) 252 (b) 257 (c) 504 (d) 48
  38. 38.What is the 20th term of the AP 3, 10, 17, 24, …? (a) 133 (b) 136 (c) 140 (d) 143
  39. 39.What is the sum of the first 11 terms of the AP 5, 7, 9, …? (a) 176 (b) 330 (c) 25 (d) 165
  40. 40.Which term of the AP 4, 10, 16, 22, … is 70? (a) 12th (b) 11th (c) 14th (d) 13th

Answer key

  1. 8th
  2. 124
  3. 65
  4. 26
  5. 66
  6. 4560
  7. 81
  8. 400
  9. 256
  10. 17th
  11. 28
  12. 180
  13. 67
  14. 1176
  15. 25th
  16. 2278
  17. 65
  18. 109
  19. 676
  20. 33rd
  21. 15
  22. 28th
  23. 202
  24. 12
  25. 741
  26. 162
  27. 150
  28. 90
  29. 352
  30. 297
  31. 123
  32. 119
  33. 841
  34. 97
  35. 625
  36. 153
  37. 252
  38. 136
  39. 165
  40. 12th

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