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Arithmetic Progression Worksheet for Olympiad

Maths Olympiad topic 29: Sequences and AP · Set 543 · 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 31st term of the AP 12, 21, 30, 39, …? (a) 270 (b) 282 (c) 279 (d) 291
  2. 2.What is the sum of all the whole numbers from 1 to 45? (a) 990 (b) 1035 (c) 1036 (d) 2070
  3. 3.What is the sum of the first 11 terms of the AP 3, 5, 7, …? (a) 154 (b) 143 (c) 286 (d) 23
  4. 4.What is the 17th term of the AP 5, 11, 17, 23, …? (a) 96 (b) 101 (c) 102 (d) 107
  5. 5.What is the sum of the first 7 terms of the AP 8, 10, 12, …? (a) 196 (b) 105 (c) 98 (d) 20
  6. 6.What is the sum of the first 20 odd numbers (1 + 3 + 5 + …)? (a) 210 (b) 400 (c) 39 (d) 420
  7. 7.What is the 19th term of the AP 4, 10, 16, 22, …? (a) 118 (b) 114 (c) 108 (d) 112
  8. 8.What is the missing term in the AP 7, ?, 13, 16, 19? (a) 9 (b) 11 (c) 13 (d) 10
  9. 9.What is the 23rd term of the AP 19, 28, 37, 46, …? (a) 207 (b) 198 (c) 217 (d) 226
  10. 10.What is the sum of the first 5 terms of the AP 9, 13, 17, …? (a) 170 (b) 95 (c) 85 (d) 25
  11. 11.What is the 33rd term of the AP 18, 24, 30, 36, …? (a) 198 (b) 210 (c) 216 (d) 192
  12. 12.What is the 14th term of the AP 2, 4, 6, 8, …? (a) 26 (b) 29 (c) 28 (d) 30
  13. 13.What is the sum of the first 13 odd numbers (1 + 3 + 5 + …)? (a) 91 (b) 182 (c) 169 (d) 25
  14. 14.Which term of the AP 15, 19, 23, 27, … is 47? (a) 9th (b) 8th (c) 10th (d) 11th
  15. 15.What is the sum of all the whole numbers from 1 to 47? (a) 2256 (b) 1081 (c) 1129 (d) 1128
  16. 16.What is the 36th term of the AP 17, 20, 23, 26, …? (a) 125 (b) 108 (c) 105 (d) 122
  17. 17.What is the sum of the first 5 terms of the AP 3, 4, 5, …? (a) 7 (b) 50 (c) 25 (d) 26
  18. 18.What is the sum of the first 9 terms of the AP 1, 6, 11, …? (a) 194 (b) 41 (c) 189 (d) 378
  19. 19.What is the sum of the first 7 terms of the AP 8, 14, 20, …? (a) 44 (b) 203 (c) 182 (d) 364
  20. 20.What is the 36th term of the AP 18, 24, 30, 36, …? (a) 210 (b) 216 (c) 228 (d) 234
  21. 21.What is the sum of the first 11 terms of the AP 6, 11, 16, …? (a) 341 (b) 346 (c) 682 (d) 56
  22. 22.What is the 18th term of the AP 4, 10, 16, 22, …? (a) 106 (b) 112 (c) 108 (d) 102
  23. 23.What is the 23rd term of the AP 1, 5, 9, 13, …? (a) 92 (b) 88 (c) 89 (d) 93
  24. 24.What is the missing term in the AP 5, 11, ?, 23, 29? (a) 23 (b) 16 (c) 18 (d) 17
  25. 25.What is the 22nd term of the AP 5, 14, 23, 32, …? (a) 203 (b) 189 (c) 198 (d) 194
  26. 26.What is the sum of the first 15 odd numbers (1 + 3 + 5 + …)? (a) 225 (b) 29 (c) 240 (d) 120
  27. 27.What is the 29th term of the AP 13, 18, 23, 28, …? (a) 158 (b) 145 (c) 140 (d) 153
  28. 28.What is the 22nd term of the AP 19, 22, 25, 28, …? (a) 66 (b) 85 (c) 82 (d) 63
  29. 29.What is the 34th term of the AP 17, 19, 21, 23, …? (a) 83 (b) 66 (c) 85 (d) 68
  30. 30.What is the sum of the first 22 odd numbers (1 + 3 + 5 + …)? (a) 253 (b) 43 (c) 484 (d) 506
  31. 31.What is the missing term in the AP 4, 6, ?, 10, 12? (a) 10 (b) 9 (c) 8 (d) 7
  32. 32.What is the 12th term of the AP 12, 21, 30, 39, …? (a) 99 (b) 108 (c) 111 (d) 120
  33. 33.What is the 13th term of the AP 9, 11, 13, 15, …? (a) 26 (b) 35 (c) 33 (d) 24
  34. 34.Which term of the AP 10, 15, 20, 25, … is 50? (a) 8th (b) 9th (c) 11th (d) 10th
  35. 35.What is the 16th term of the AP 11, 17, 23, 29, …? (a) 101 (b) 107 (c) 90 (d) 96
  36. 36.What is the sum of all the whole numbers from 1 to 96? (a) 4608 (b) 9312 (c) 4656 (d) 4560
  37. 37.What is the sum of the first 6 terms of the AP 10, 15, 20, …? (a) 35 (b) 270 (c) 135 (d) 150
  38. 38.What is the 33rd term of the AP 13, 21, 29, 37, …? (a) 264 (b) 256 (c) 269 (d) 277
  39. 39.What is the 31st term of the AP 1, 10, 19, 28, …? (a) 270 (b) 280 (c) 279 (d) 271
  40. 40.What is the missing term in the AP 20, 25, 30, ?, 40? (a) 36 (b) 35 (c) 34 (d) 40

Answer key

  1. 282
  2. 1035
  3. 143
  4. 101
  5. 98
  6. 400
  7. 112
  8. 10
  9. 217
  10. 85
  11. 210
  12. 28
  13. 169
  14. 9th
  15. 1128
  16. 122
  17. 25
  18. 189
  19. 182
  20. 228
  21. 341
  22. 106
  23. 89
  24. 17
  25. 194
  26. 225
  27. 153
  28. 82
  29. 83
  30. 484
  31. 8
  32. 111
  33. 33
  34. 9th
  35. 101
  36. 4656
  37. 135
  38. 269
  39. 271
  40. 35

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