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Arithmetic Progression Worksheet for Olympiad

Maths Olympiad topic 29: Sequences and AP · Set 377 · 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 15th term of the AP 12, 20, 28, 36, …? (a) 132 (b) 112 (c) 120 (d) 124
  2. 2.What is the missing term in the AP 10, 15, ?, 25, 30? (a) 21 (b) 19 (c) 20 (d) 25
  3. 3.What is the 29th term of the AP 15, 24, 33, 42, …? (a) 261 (b) 276 (c) 267 (d) 252
  4. 4.What is the sum of all the whole numbers from 1 to 18? (a) 342 (b) 162 (c) 171 (d) 153
  5. 5.What is the sum of all the whole numbers from 1 to 33? (a) 561 (b) 528 (c) 562 (d) 1122
  6. 6.What is the 18th term of the AP 9, 15, 21, 27, …? (a) 111 (b) 102 (c) 117 (d) 108
  7. 7.What is the sum of the first 13 odd numbers (1 + 3 + 5 + …)? (a) 182 (b) 25 (c) 91 (d) 169
  8. 8.What is the sum of all the whole numbers from 1 to 92? (a) 4278 (b) 4232 (c) 4186 (d) 8556
  9. 9.What is the sum of the first 16 odd numbers (1 + 3 + 5 + …)? (a) 31 (b) 272 (c) 136 (d) 256
  10. 10.What is the 33rd term of the AP 6, 15, 24, 33, …? (a) 303 (b) 297 (c) 288 (d) 294
  11. 11.What is the sum of the first 6 terms of the AP 1, 2, 3, …? (a) 21 (b) 24 (c) 6 (d) 42
  12. 12.What is the missing term in the AP 12, ?, 24, 30, 36? (a) 24 (b) 19 (c) 17 (d) 18
  13. 13.What is the sum of all the whole numbers from 1 to 20? (a) 420 (b) 200 (c) 210 (d) 190
  14. 14.What is the sum of the first 9 terms of the AP 4, 10, 16, …? (a) 52 (b) 504 (c) 279 (d) 252
  15. 15.What is the missing term in the AP 10, ?, 14, 16, 18? (a) 11 (b) 13 (c) 12 (d) 14
  16. 16.What is the sum of the first 8 odd numbers (1 + 3 + 5 + …)? (a) 36 (b) 64 (c) 72 (d) 15
  17. 17.What is the 14th term of the AP 7, 15, 23, 31, …? (a) 104 (b) 119 (c) 111 (d) 112
  18. 18.What is the missing term in the AP 1, 7, ?, 19, 25? (a) 13 (b) 19 (c) 14 (d) 12
  19. 19.What is the sum of the first 5 terms of the AP 1, 5, 9, …? (a) 45 (b) 90 (c) 55 (d) 17
  20. 20.What is the missing term in the AP 3, 12, ?, 30, 39? (a) 20 (b) 22 (c) 30 (d) 21
  21. 21.What is the sum of the first 15 odd numbers (1 + 3 + 5 + …)? (a) 29 (b) 225 (c) 240 (d) 120
  22. 22.What is the sum of the first 10 terms of the AP 9, 10, 11, …? (a) 135 (b) 18 (c) 140 (d) 270
  23. 23.What is the sum of the first 11 terms of the AP 9, 10, 11, …? (a) 308 (b) 19 (c) 154 (d) 155
  24. 24.What is the sum of the first 22 odd numbers (1 + 3 + 5 + …)? (a) 43 (b) 484 (c) 506 (d) 253
  25. 25.What is the 40th term of the AP 19, 23, 27, 31, …? (a) 156 (b) 160 (c) 179 (d) 175
  26. 26.What is the sum of all the whole numbers from 1 to 26? (a) 325 (b) 338 (c) 351 (d) 702
  27. 27.What is the 13th term of the AP 16, 23, 30, 37, …? (a) 91 (b) 107 (c) 84 (d) 100
  28. 28.What is the 27th term of the AP 20, 29, 38, 47, …? (a) 254 (b) 234 (c) 263 (d) 243
  29. 29.What is the missing term in the AP 3, ?, 13, 18, 23? (a) 13 (b) 7 (c) 9 (d) 8
  30. 30.What is the sum of all the whole numbers from 1 to 98? (a) 9702 (b) 4802 (c) 4851 (d) 4753
  31. 31.What is the missing term in the AP 9, 18, 27, ?, 45? (a) 35 (b) 36 (c) 37 (d) 45
  32. 32.What is the sum of all the whole numbers from 1 to 38? (a) 703 (b) 722 (c) 741 (d) 1482
  33. 33.What is the sum of the first 25 odd numbers (1 + 3 + 5 + …)? (a) 625 (b) 325 (c) 650 (d) 49
  34. 34.What is the 24th term of the AP 14, 16, 18, 20, …? (a) 60 (b) 46 (c) 62 (d) 48
  35. 35.What is the sum of the first 12 odd numbers (1 + 3 + 5 + …)? (a) 144 (b) 23 (c) 78 (d) 156
  36. 36.What is the 24th term of the AP 13, 19, 25, 31, …? (a) 151 (b) 157 (c) 138 (d) 144
  37. 37.What is the 26th term of the AP 20, 24, 28, 32, …? (a) 120 (b) 104 (c) 100 (d) 124
  38. 38.What is the sum of the first 9 terms of the AP 1, 6, 11, …? (a) 378 (b) 194 (c) 41 (d) 189
  39. 39.What is the missing term in the AP 13, 20, 27, ?, 41? (a) 35 (b) 33 (c) 41 (d) 34
  40. 40.What is the missing term in the AP 5, 13, 21, ?, 37? (a) 30 (b) 29 (c) 28 (d) 37

Answer key

  1. 124
  2. 20
  3. 267
  4. 171
  5. 561
  6. 111
  7. 169
  8. 4278
  9. 256
  10. 294
  11. 21
  12. 18
  13. 210
  14. 252
  15. 12
  16. 64
  17. 111
  18. 13
  19. 45
  20. 21
  21. 225
  22. 135
  23. 154
  24. 484
  25. 175
  26. 351
  27. 100
  28. 254
  29. 8
  30. 4851
  31. 36
  32. 741
  33. 625
  34. 60
  35. 144
  36. 151
  37. 120
  38. 189
  39. 34
  40. 29

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