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Arithmetic Progression Worksheet for Olympiad

Maths Olympiad topic 29: Sequences and AP · Set 723 · 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 26th term of the AP 9, 12, 15, 18, …? (a) 78 (b) 84 (c) 75 (d) 87
  2. 2.What is the sum of the first 10 terms of the AP 3, 9, 15, …? (a) 57 (b) 300 (c) 600 (d) 330
  3. 3.What is the missing term in the AP 4, ?, 10, 13, 16? (a) 6 (b) 8 (c) 10 (d) 7
  4. 4.What is the missing term in the AP 19, 25, 31, ?, 43? (a) 37 (b) 38 (c) 43 (d) 36
  5. 5.What is the 22nd term of the AP 17, 21, 25, 29, …? (a) 105 (b) 101 (c) 88 (d) 84
  6. 6.What is the sum of all the whole numbers from 1 to 56? (a) 1540 (b) 1596 (c) 1568 (d) 3192
  7. 7.What is the 33rd term of the AP 3, 12, 21, 30, …? (a) 291 (b) 288 (c) 300 (d) 297
  8. 8.What is the sum of the first 18 odd numbers (1 + 3 + 5 + …)? (a) 171 (b) 35 (c) 324 (d) 342
  9. 9.Which term of the AP 5, 11, 17, 23, … is 233? (a) 41st (b) 39th (c) 38th (d) 40th
  10. 10.What is the sum of all the whole numbers from 1 to 35? (a) 630 (b) 1260 (c) 595 (d) 631
  11. 11.What is the 22nd term of the AP 8, 15, 22, 29, …? (a) 162 (b) 154 (c) 147 (d) 155
  12. 12.What is the sum of the first 26 odd numbers (1 + 3 + 5 + …)? (a) 351 (b) 51 (c) 676 (d) 702
  13. 13.What is the 29th term of the AP 5, 12, 19, 26, …? (a) 196 (b) 208 (c) 203 (d) 201
  14. 14.What is the missing term in the AP 13, 17, ?, 25, 29? (a) 22 (b) 25 (c) 21 (d) 20
  15. 15.What is the sum of the first 19 odd numbers (1 + 3 + 5 + …)? (a) 37 (b) 361 (c) 380 (d) 190
  16. 16.What is the missing term in the AP 4, 9, ?, 19, 24? (a) 13 (b) 19 (c) 14 (d) 15
  17. 17.What is the sum of the first 10 terms of the AP 3, 4, 5, …? (a) 150 (b) 12 (c) 80 (d) 75
  18. 18.What is the missing term in the AP 5, 7, 9, ?, 13? (a) 11 (b) 10 (c) 13 (d) 12
  19. 19.What is the 38th term of the AP 14, 20, 26, 32, …? (a) 228 (b) 222 (c) 242 (d) 236
  20. 20.What is the sum of all the whole numbers from 1 to 71? (a) 2485 (b) 2556 (c) 2557 (d) 5112
  21. 21.What is the sum of the first 25 odd numbers (1 + 3 + 5 + …)? (a) 325 (b) 49 (c) 625 (d) 650
  22. 22.What is the 24th term of the AP 16, 18, 20, 22, …? (a) 64 (b) 48 (c) 46 (d) 62
  23. 23.What is the missing term in the AP 11, 14, 17, ?, 23? (a) 19 (b) 21 (c) 23 (d) 20
  24. 24.What is the sum of all the whole numbers from 1 to 12? (a) 66 (b) 156 (c) 78 (d) 72
  25. 25.What is the sum of the first 10 odd numbers (1 + 3 + 5 + …)? (a) 100 (b) 110 (c) 19 (d) 55
  26. 26.What is the 12th term of the AP 1, 4, 7, 10, …? (a) 37 (b) 33 (c) 36 (d) 34
  27. 27.What is the sum of the first 8 odd numbers (1 + 3 + 5 + …)? (a) 72 (b) 15 (c) 36 (d) 64
  28. 28.What is the 26th term of the AP 3, 5, 7, 9, …? (a) 50 (b) 55 (c) 52 (d) 53
  29. 29.What is the 24th term of the AP 13, 21, 29, 37, …? (a) 205 (b) 192 (c) 184 (d) 197
  30. 30.What is the missing term in the AP 11, ?, 21, 26, 31? (a) 16 (b) 21 (c) 15 (d) 17
  31. 31.Which term of the AP 11, 18, 25, 32, … is 60? (a) 10th (b) 9th (c) 7th (d) 8th
  32. 32.What is the sum of the first 8 terms of the AP 4, 9, 14, …? (a) 39 (b) 192 (c) 172 (d) 344
  33. 33.Which term of the AP 18, 24, 30, 36, … is 204? (a) 33rd (b) 32nd (c) 34th (d) 31st
  34. 34.What is the sum of the first 9 terms of the AP 3, 5, 7, …? (a) 99 (b) 19 (c) 198 (d) 108
  35. 35.What is the 36th term of the AP 15, 21, 27, 33, …? (a) 210 (b) 231 (c) 216 (d) 225
  36. 36.What is the sum of the first 13 odd numbers (1 + 3 + 5 + …)? (a) 182 (b) 25 (c) 91 (d) 169
  37. 37.What is the missing term in the AP 11, 18, ?, 32, 39? (a) 24 (b) 32 (c) 25 (d) 26
  38. 38.What is the missing term in the AP 16, ?, 22, 25, 28? (a) 19 (b) 18 (c) 22 (d) 20
  39. 39.What is the 39th term of the AP 17, 23, 29, 35, …? (a) 228 (b) 234 (c) 245 (d) 251
  40. 40.What is the sum of all the whole numbers from 1 to 10? (a) 110 (b) 50 (c) 45 (d) 55

Answer key

  1. 84
  2. 300
  3. 7
  4. 37
  5. 101
  6. 1596
  7. 291
  8. 324
  9. 39th
  10. 630
  11. 155
  12. 676
  13. 201
  14. 21
  15. 361
  16. 14
  17. 75
  18. 11
  19. 236
  20. 2556
  21. 625
  22. 62
  23. 20
  24. 78
  25. 100
  26. 34
  27. 64
  28. 53
  29. 197
  30. 16
  31. 8th
  32. 172
  33. 32nd
  34. 99
  35. 225
  36. 169
  37. 25
  38. 19
  39. 245
  40. 55

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