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Arithmetic Progression Worksheet for Olympiad

Maths Olympiad topic 29: Sequences and AP · Set 297 · 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 sum of all the whole numbers from 1 to 42? (a) 882 (b) 903 (c) 1806 (d) 861
  2. 2.What is the sum of all the whole numbers from 1 to 20? (a) 200 (b) 420 (c) 190 (d) 210
  3. 3.What is the sum of the first 11 odd numbers (1 + 3 + 5 + …)? (a) 121 (b) 21 (c) 132 (d) 66
  4. 4.What is the 14th term of the AP 3, 10, 17, 24, …? (a) 101 (b) 94 (c) 98 (d) 91
  5. 5.What is the 11th term of the AP 8, 13, 18, 23, …? (a) 63 (b) 55 (c) 58 (d) 50
  6. 6.What is the sum of the first 7 terms of the AP 9, 10, 11, …? (a) 85 (b) 15 (c) 168 (d) 84
  7. 7.What is the missing term in the AP 6, ?, 22, 30, 38? (a) 13 (b) 15 (c) 14 (d) 22
  8. 8.What is the 32nd term of the AP 3, 6, 9, 12, …? (a) 97 (b) 93 (c) 99 (d) 96
  9. 9.What is the sum of the first 11 terms of the AP 4, 7, 10, …? (a) 209 (b) 212 (c) 418 (d) 34
  10. 10.What is the missing term in the AP 17, 19, ?, 23, 25? (a) 22 (b) 20 (c) 21 (d) 23
  11. 11.What is the 27th term of the AP 18, 24, 30, 36, …? (a) 162 (b) 156 (c) 180 (d) 174
  12. 12.What is the 16th term of the AP 20, 22, 24, 26, …? (a) 52 (b) 50 (c) 30 (d) 32
  13. 13.What is the sum of all the whole numbers from 1 to 15? (a) 121 (b) 240 (c) 105 (d) 120
  14. 14.What is the sum of all the whole numbers from 1 to 14? (a) 98 (b) 210 (c) 105 (d) 91
  15. 15.What is the 40th term of the AP 4, 11, 18, 25, …? (a) 280 (b) 284 (c) 273 (d) 277
  16. 16.What is the 15th term of the AP 16, 21, 26, 31, …? (a) 86 (b) 70 (c) 75 (d) 91
  17. 17.What is the missing term in the AP 2, 7, ?, 17, 22? (a) 17 (b) 11 (c) 12 (d) 13
  18. 18.What is the missing term in the AP 20, 27, 34, ?, 48? (a) 48 (b) 42 (c) 41 (d) 40
  19. 19.Which term of the AP 16, 21, 26, 31, … is 71? (a) 14th (b) 12th (c) 13th (d) 11th
  20. 20.What is the missing term in the AP 16, 20, ?, 28, 32? (a) 24 (b) 25 (c) 28 (d) 23
  21. 21.What is the sum of the first 12 terms of the AP 4, 8, 12, …? (a) 336 (b) 312 (c) 48 (d) 624
  22. 22.What is the missing term in the AP 14, 22, 30, ?, 46? (a) 46 (b) 38 (c) 37 (d) 39
  23. 23.What is the sum of the first 10 terms of the AP 9, 11, 13, …? (a) 360 (b) 190 (c) 180 (d) 27
  24. 24.What is the 36th term of the AP 12, 20, 28, 36, …? (a) 300 (b) 280 (c) 292 (d) 288
  25. 25.What is the sum of the first 8 terms of the AP 8, 10, 12, …? (a) 240 (b) 22 (c) 120 (d) 128
  26. 26.Which term of the AP 2, 9, 16, 23, … is 254? (a) 38th (b) 39th (c) 37th (d) 36th
  27. 27.What is the sum of the first 22 odd numbers (1 + 3 + 5 + …)? (a) 506 (b) 253 (c) 43 (d) 484
  28. 28.What is the sum of the first 10 terms of the AP 3, 7, 11, …? (a) 420 (b) 39 (c) 210 (d) 230
  29. 29.What is the 10th term of the AP 15, 19, 23, 27, …? (a) 40 (b) 55 (c) 51 (d) 36
  30. 30.What is the sum of the first 6 terms of the AP 5, 10, 15, …? (a) 30 (b) 120 (c) 105 (d) 210
  31. 31.What is the 13th term of the AP 5, 13, 21, 29, …? (a) 104 (b) 109 (c) 96 (d) 101
  32. 32.What is the 19th term of the AP 4, 7, 10, 13, …? (a) 57 (b) 54 (c) 58 (d) 61
  33. 33.What is the sum of all the whole numbers from 1 to 50? (a) 1275 (b) 1250 (c) 2550 (d) 1225
  34. 34.What is the sum of the first 11 terms of the AP 8, 13, 18, …? (a) 58 (b) 368 (c) 726 (d) 363
  35. 35.What is the sum of the first 10 terms of the AP 2, 3, 4, …? (a) 130 (b) 11 (c) 70 (d) 65
  36. 36.What is the sum of the first 7 terms of the AP 4, 10, 16, …? (a) 154 (b) 308 (c) 40 (d) 175
  37. 37.What is the sum of all the whole numbers from 1 to 82? (a) 3403 (b) 3362 (c) 6806 (d) 3321
  38. 38.What is the 23rd term of the AP 5, 9, 13, 17, …? (a) 97 (b) 88 (c) 92 (d) 93
  39. 39.What is the sum of the first 6 terms of the AP 6, 12, 18, …? (a) 252 (b) 126 (c) 36 (d) 144
  40. 40.What is the sum of the first 9 terms of the AP 3, 6, 9, …? (a) 138 (b) 270 (c) 27 (d) 135

Answer key

  1. 903
  2. 210
  3. 121
  4. 94
  5. 58
  6. 84
  7. 14
  8. 96
  9. 209
  10. 21
  11. 174
  12. 50
  13. 120
  14. 105
  15. 277
  16. 86
  17. 12
  18. 41
  19. 12th
  20. 24
  21. 312
  22. 38
  23. 180
  24. 292
  25. 120
  26. 37th
  27. 484
  28. 210
  29. 51
  30. 105
  31. 101
  32. 58
  33. 1275
  34. 363
  35. 65
  36. 154
  37. 3403
  38. 93
  39. 126
  40. 135

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