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Arithmetic Progression Worksheet for Olympiad

Maths Olympiad topic 29: Sequences and AP · Set 392 · 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 17th term of the AP 15, 20, 25, 30, …? (a) 100 (b) 85 (c) 80 (d) 95
  2. 2.Which term of the AP 15, 24, 33, 42, … is 123? (a) 12th (b) 13th (c) 14th (d) 15th
  3. 3.What is the sum of the first 6 terms of the AP 10, 13, 16, …? (a) 114 (b) 210 (c) 25 (d) 105
  4. 4.What is the sum of the first 9 terms of the AP 3, 6, 9, …? (a) 270 (b) 135 (c) 138 (d) 27
  5. 5.What is the 18th term of the AP 14, 23, 32, 41, …? (a) 153 (b) 162 (c) 167 (d) 176
  6. 6.What is the 36th term of the AP 1, 7, 13, 19, …? (a) 210 (b) 216 (c) 211 (d) 217
  7. 7.What is the sum of the first 11 terms of the AP 2, 6, 10, …? (a) 484 (b) 264 (c) 242 (d) 42
  8. 8.What is the missing term in the AP 11, 19, 27, ?, 43? (a) 43 (b) 36 (c) 35 (d) 34
  9. 9.What is the sum of the first 8 odd numbers (1 + 3 + 5 + …)? (a) 64 (b) 72 (c) 36 (d) 15
  10. 10.What is the missing term in the AP 12, 14, 16, ?, 20? (a) 19 (b) 20 (c) 17 (d) 18
  11. 11.What is the sum of the first 12 terms of the AP 4, 10, 16, …? (a) 70 (b) 888 (c) 444 (d) 480
  12. 12.What is the sum of the first 9 terms of the AP 2, 4, 6, …? (a) 99 (b) 90 (c) 18 (d) 180
  13. 13.What is the sum of the first 10 terms of the AP 8, 13, 18, …? (a) 53 (b) 305 (c) 610 (d) 330
  14. 14.What is the sum of the first 6 terms of the AP 6, 12, 18, …? (a) 144 (b) 36 (c) 126 (d) 252
  15. 15.What is the sum of the first 10 terms of the AP 8, 9, 10, …? (a) 250 (b) 130 (c) 17 (d) 125
  16. 16.What is the sum of all the whole numbers from 1 to 48? (a) 1152 (b) 1128 (c) 1176 (d) 2352
  17. 17.What is the missing term in the AP 17, ?, 21, 23, 25? (a) 20 (b) 21 (c) 19 (d) 18
  18. 18.What is the sum of the first 6 terms of the AP 7, 10, 13, …? (a) 87 (b) 96 (c) 174 (d) 22
  19. 19.What is the missing term in the AP 3, ?, 21, 30, 39? (a) 21 (b) 12 (c) 11 (d) 13
  20. 20.What is the 27th term of the AP 12, 14, 16, 18, …? (a) 66 (b) 52 (c) 54 (d) 64
  21. 21.What is the 35th term of the AP 3, 12, 21, 30, …? (a) 315 (b) 306 (c) 318 (d) 309
  22. 22.Which term of the AP 2, 9, 16, 23, … is 65? (a) 11th (b) 9th (c) 12th (d) 10th
  23. 23.What is the 23rd term of the AP 1, 5, 9, 13, …? (a) 93 (b) 88 (c) 92 (d) 89
  24. 24.What is the 12th term of the AP 2, 7, 12, 17, …? (a) 60 (b) 57 (c) 55 (d) 62
  25. 25.What is the sum of the first 12 terms of the AP 3, 7, 11, …? (a) 600 (b) 324 (c) 300 (d) 47
  26. 26.What is the sum of the first 22 odd numbers (1 + 3 + 5 + …)? (a) 253 (b) 484 (c) 43 (d) 506
  27. 27.What is the sum of the first 8 terms of the AP 3, 5, 7, …? (a) 80 (b) 160 (c) 88 (d) 17
  28. 28.What is the sum of all the whole numbers from 1 to 70? (a) 2450 (b) 4970 (c) 2415 (d) 2485
  29. 29.What is the 12th term of the AP 4, 6, 8, 10, …? (a) 26 (b) 24 (c) 22 (d) 28
  30. 30.What is the sum of the first 9 terms of the AP 8, 12, 16, …? (a) 432 (b) 234 (c) 216 (d) 40
  31. 31.What is the sum of the first 5 terms of the AP 2, 3, 4, …? (a) 20 (b) 40 (c) 6 (d) 21
  32. 32.What is the sum of all the whole numbers from 1 to 94? (a) 4418 (b) 8930 (c) 4371 (d) 4465
  33. 33.Which term of the AP 11, 18, 25, 32, … is 109? (a) 16th (b) 14th (c) 15th (d) 17th
  34. 34.What is the sum of the first 29 odd numbers (1 + 3 + 5 + …)? (a) 841 (b) 870 (c) 435 (d) 57
  35. 35.Which term of the AP 5, 14, 23, 32, … is 194? (a) 23rd (b) 21st (c) 22nd (d) 24th
  36. 36.What is the sum of the first 24 odd numbers (1 + 3 + 5 + …)? (a) 576 (b) 600 (c) 47 (d) 300
  37. 37.What is the sum of the first 9 odd numbers (1 + 3 + 5 + …)? (a) 45 (b) 17 (c) 90 (d) 81
  38. 38.What is the 22nd term of the AP 19, 22, 25, 28, …? (a) 85 (b) 63 (c) 66 (d) 82
  39. 39.What is the missing term in the AP 10, 13, ?, 19, 22? (a) 19 (b) 17 (c) 15 (d) 16
  40. 40.What is the sum of all the whole numbers from 1 to 56? (a) 1568 (b) 1540 (c) 1596 (d) 3192

Answer key

  1. 95
  2. 13th
  3. 105
  4. 135
  5. 167
  6. 211
  7. 242
  8. 35
  9. 64
  10. 18
  11. 444
  12. 90
  13. 305
  14. 126
  15. 125
  16. 1176
  17. 19
  18. 87
  19. 12
  20. 64
  21. 309
  22. 10th
  23. 89
  24. 57
  25. 300
  26. 484
  27. 80
  28. 2485
  29. 26
  30. 216
  31. 20
  32. 4465
  33. 15th
  34. 841
  35. 22nd
  36. 576
  37. 81
  38. 82
  39. 16
  40. 1596

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