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Arithmetic Progression Worksheet for Olympiad

Maths Olympiad topic 29: Sequences and AP · Set 138 · 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 the first 9 terms of the AP 2, 4, 6, …? (a) 18 (b) 90 (c) 180 (d) 99
  2. 2.What is the 40th term of the AP 20, 29, 38, 47, …? (a) 351 (b) 371 (c) 380 (d) 360
  3. 3.What is the sum of all the whole numbers from 1 to 86? (a) 7482 (b) 3698 (c) 3741 (d) 3655
  4. 4.What is the 22nd term of the AP 3, 9, 15, 21, …? (a) 126 (b) 135 (c) 132 (d) 129
  5. 5.What is the sum of the first 11 terms of the AP 10, 16, 22, …? (a) 473 (b) 70 (c) 880 (d) 440
  6. 6.What is the sum of the first 28 odd numbers (1 + 3 + 5 + …)? (a) 55 (b) 406 (c) 812 (d) 784
  7. 7.What is the 26th term of the AP 4, 8, 12, 16, …? (a) 104 (b) 100 (c) 108 (d) 105
  8. 8.What is the missing term in the AP 14, 18, 22, ?, 30? (a) 27 (b) 30 (c) 26 (d) 25
  9. 9.What is the sum of the first 9 terms of the AP 9, 10, 11, …? (a) 118 (b) 117 (c) 17 (d) 234
  10. 10.What is the sum of the first 11 terms of the AP 4, 9, 14, …? (a) 54 (b) 319 (c) 638 (d) 324
  11. 11.What is the 10th term of the AP 5, 9, 13, 17, …? (a) 41 (b) 40 (c) 36 (d) 45
  12. 12.What is the 24th term of the AP 6, 14, 22, 30, …? (a) 192 (b) 190 (c) 198 (d) 184
  13. 13.What is the 23rd term of the AP 11, 20, 29, 38, …? (a) 218 (b) 207 (c) 198 (d) 209
  14. 14.What is the missing term in the AP 14, 16, 18, ?, 22? (a) 19 (b) 22 (c) 21 (d) 20
  15. 15.What is the sum of all the whole numbers from 1 to 23? (a) 276 (b) 253 (c) 552 (d) 277
  16. 16.What is the 36th term of the AP 4, 13, 22, 31, …? (a) 324 (b) 319 (c) 315 (d) 328
  17. 17.Which term of the AP 5, 7, 9, 11, … is 27? (a) 11th (b) 14th (c) 12th (d) 13th
  18. 18.What is the missing term in the AP 5, 8, ?, 14, 17? (a) 10 (b) 12 (c) 11 (d) 14
  19. 19.What is the sum of the first 6 terms of the AP 2, 3, 4, …? (a) 54 (b) 7 (c) 30 (d) 27
  20. 20.What is the 13th term of the AP 12, 15, 18, 21, …? (a) 51 (b) 36 (c) 39 (d) 48
  21. 21.What is the sum of the first 10 terms of the AP 1, 2, 3, …? (a) 10 (b) 110 (c) 55 (d) 60
  22. 22.What is the 28th term of the AP 5, 8, 11, 14, …? (a) 89 (b) 84 (c) 86 (d) 81
  23. 23.What is the sum of the first 25 odd numbers (1 + 3 + 5 + …)? (a) 325 (b) 650 (c) 625 (d) 49
  24. 24.What is the sum of all the whole numbers from 1 to 24? (a) 276 (b) 600 (c) 300 (d) 288
  25. 25.What is the sum of all the whole numbers from 1 to 57? (a) 1654 (b) 1596 (c) 3306 (d) 1653
  26. 26.What is the sum of the first 8 terms of the AP 9, 14, 19, …? (a) 424 (b) 212 (c) 44 (d) 232
  27. 27.What is the 16th term of the AP 13, 18, 23, 28, …? (a) 88 (b) 93 (c) 80 (d) 75
  28. 28.What is the sum of the first 13 odd numbers (1 + 3 + 5 + …)? (a) 25 (b) 91 (c) 182 (d) 169
  29. 29.What is the 36th term of the AP 3, 11, 19, 27, …? (a) 283 (b) 288 (c) 280 (d) 291
  30. 30.What is the missing term in the AP 5, 8, 11, ?, 17? (a) 13 (b) 17 (c) 15 (d) 14
  31. 31.What is the sum of the first 5 terms of the AP 4, 7, 10, …? (a) 53 (b) 100 (c) 50 (d) 16
  32. 32.What is the 22nd term of the AP 12, 20, 28, 36, …? (a) 168 (b) 176 (c) 188 (d) 180
  33. 33.What is the sum of the first 16 odd numbers (1 + 3 + 5 + …)? (a) 136 (b) 31 (c) 256 (d) 272
  34. 34.What is the sum of the first 12 terms of the AP 10, 11, 12, …? (a) 372 (b) 192 (c) 186 (d) 21
  35. 35.What is the missing term in the AP 3, 6, 9, ?, 15? (a) 11 (b) 12 (c) 13 (d) 15
  36. 36.What is the sum of the first 10 terms of the AP 7, 8, 9, …? (a) 16 (b) 115 (c) 230 (d) 120
  37. 37.What is the sum of the first 8 odd numbers (1 + 3 + 5 + …)? (a) 36 (b) 72 (c) 15 (d) 64
  38. 38.What is the missing term in the AP 16, 23, 30, ?, 44? (a) 36 (b) 44 (c) 38 (d) 37
  39. 39.What is the 25th term of the AP 12, 21, 30, 39, …? (a) 228 (b) 225 (c) 216 (d) 237
  40. 40.Which term of the AP 4, 12, 20, 28, … is 196? (a) 27th (b) 25th (c) 26th (d) 24th

Answer key

  1. 90
  2. 371
  3. 3741
  4. 129
  5. 440
  6. 784
  7. 104
  8. 26
  9. 117
  10. 319
  11. 41
  12. 190
  13. 209
  14. 20
  15. 276
  16. 319
  17. 12th
  18. 11
  19. 27
  20. 48
  21. 55
  22. 86
  23. 625
  24. 300
  25. 1653
  26. 212
  27. 88
  28. 169
  29. 283
  30. 14
  31. 50
  32. 180
  33. 256
  34. 186
  35. 12
  36. 115
  37. 64
  38. 37
  39. 228
  40. 25th

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