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Arithmetic Progression Worksheet for Olympiad

Maths Olympiad topic 29: Sequences and AP · Set 257 · 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 18th term of the AP 17, 22, 27, 32, …? (a) 102 (b) 107 (c) 85 (d) 90
  2. 2.What is the 21st term of the AP 8, 17, 26, 35, …? (a) 189 (b) 197 (c) 188 (d) 180
  3. 3.What is the missing term in the AP 17, 20, ?, 26, 29? (a) 23 (b) 26 (c) 22 (d) 24
  4. 4.What is the sum of all the whole numbers from 1 to 96? (a) 4608 (b) 4560 (c) 4656 (d) 9312
  5. 5.What is the 36th term of the AP 20, 27, 34, 41, …? (a) 265 (b) 252 (c) 245 (d) 272
  6. 6.What is the sum of all the whole numbers from 1 to 52? (a) 1378 (b) 2756 (c) 1326 (d) 1352
  7. 7.What is the sum of the first 11 terms of the AP 3, 4, 5, …? (a) 88 (b) 89 (c) 176 (d) 13
  8. 8.What is the sum of the first 10 terms of the AP 10, 15, 20, …? (a) 650 (b) 55 (c) 350 (d) 325
  9. 9.What is the 18th term of the AP 3, 7, 11, 15, …? (a) 68 (b) 71 (c) 72 (d) 75
  10. 10.Which term of the AP 9, 14, 19, 24, … is 159? (a) 31st (b) 30th (c) 33rd (d) 32nd
  11. 11.What is the sum of the first 6 terms of the AP 7, 11, 15, …? (a) 204 (b) 114 (c) 102 (d) 27
  12. 12.What is the 24th term of the AP 16, 18, 20, 22, …? (a) 64 (b) 62 (c) 46 (d) 48
  13. 13.What is the sum of all the whole numbers from 1 to 15? (a) 105 (b) 121 (c) 240 (d) 120
  14. 14.What is the 12th term of the AP 20, 23, 26, 29, …? (a) 36 (b) 56 (c) 53 (d) 33
  15. 15.What is the sum of all the whole numbers from 1 to 77? (a) 3003 (b) 2926 (c) 6006 (d) 3004
  16. 16.Which term of the AP 20, 28, 36, 44, … is 148? (a) 17th (b) 16th (c) 19th (d) 18th
  17. 17.What is the sum of all the whole numbers from 1 to 32? (a) 1056 (b) 528 (c) 496 (d) 512
  18. 18.What is the sum of all the whole numbers from 1 to 73? (a) 2701 (b) 2628 (c) 5402 (d) 2702
  19. 19.What is the 40th term of the AP 13, 18, 23, 28, …? (a) 195 (b) 213 (c) 200 (d) 208
  20. 20.What is the 14th term of the AP 2, 7, 12, 17, …? (a) 70 (b) 65 (c) 67 (d) 72
  21. 21.What is the sum of the first 21 odd numbers (1 + 3 + 5 + …)? (a) 462 (b) 231 (c) 441 (d) 41
  22. 22.What is the sum of all the whole numbers from 1 to 83? (a) 3487 (b) 6972 (c) 3403 (d) 3486
  23. 23.What is the 32nd term of the AP 3, 6, 9, 12, …? (a) 99 (b) 93 (c) 97 (d) 96
  24. 24.What is the sum of the first 7 odd numbers (1 + 3 + 5 + …)? (a) 49 (b) 13 (c) 28 (d) 56
  25. 25.What is the sum of all the whole numbers from 1 to 14? (a) 98 (b) 91 (c) 210 (d) 105
  26. 26.Which term of the AP 3, 5, 7, 9, … is 57? (a) 30th (b) 29th (c) 27th (d) 28th
  27. 27.What is the 20th term of the AP 9, 18, 27, 36, …? (a) 189 (b) 180 (c) 181 (d) 171
  28. 28.What is the missing term in the AP 11, 14, 17, ?, 23? (a) 21 (b) 20 (c) 23 (d) 19
  29. 29.Which term of the AP 8, 17, 26, 35, … is 116? (a) 14th (b) 12th (c) 15th (d) 13th
  30. 30.What is the sum of the first 5 terms of the AP 8, 10, 12, …? (a) 120 (b) 60 (c) 65 (d) 16
  31. 31.What is the sum of the first 6 terms of the AP 3, 8, 13, …? (a) 108 (b) 28 (c) 93 (d) 186
  32. 32.What is the 21st term of the AP 7, 12, 17, 22, …? (a) 107 (b) 112 (c) 105 (d) 100
  33. 33.What is the 13th term of the AP 16, 19, 22, 25, …? (a) 52 (b) 39 (c) 55 (d) 36
  34. 34.What is the sum of the first 7 terms of the AP 1, 6, 11, …? (a) 112 (b) 224 (c) 31 (d) 117
  35. 35.What is the sum of the first 6 terms of the AP 10, 16, 22, …? (a) 300 (b) 168 (c) 40 (d) 150
  36. 36.What is the sum of the first 5 odd numbers (1 + 3 + 5 + …)? (a) 15 (b) 25 (c) 30 (d) 9
  37. 37.What is the sum of the first 7 terms of the AP 3, 9, 15, …? (a) 168 (b) 294 (c) 39 (d) 147
  38. 38.What is the 20th term of the AP 14, 23, 32, 41, …? (a) 171 (b) 180 (c) 194 (d) 185
  39. 39.What is the sum of the first 10 terms of the AP 3, 7, 11, …? (a) 210 (b) 39 (c) 420 (d) 230
  40. 40.Which term of the AP 15, 20, 25, 30, … is 100? (a) 18th (b) 20th (c) 17th (d) 19th

Answer key

  1. 102
  2. 188
  3. 23
  4. 4656
  5. 265
  6. 1378
  7. 88
  8. 325
  9. 71
  10. 31st
  11. 102
  12. 62
  13. 120
  14. 53
  15. 3003
  16. 17th
  17. 528
  18. 2701
  19. 208
  20. 67
  21. 441
  22. 3486
  23. 96
  24. 49
  25. 105
  26. 28th
  27. 180
  28. 20
  29. 13th
  30. 60
  31. 93
  32. 107
  33. 52
  34. 112
  35. 150
  36. 25
  37. 147
  38. 185
  39. 210
  40. 18th

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