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Arithmetic Progression Worksheet for Olympiad

Maths Olympiad topic 29: Sequences and AP · Set 521 · 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 30th term of the AP 3, 12, 21, 30, …? (a) 273 (b) 264 (c) 261 (d) 270
  2. 2.Which term of the AP 16, 19, 22, 25, … is 115? (a) 34th (b) 35th (c) 33rd (d) 36th
  3. 3.What is the sum of the first 10 terms of the AP 8, 13, 18, …? (a) 53 (b) 305 (c) 330 (d) 610
  4. 4.What is the 39th term of the AP 20, 24, 28, 32, …? (a) 156 (b) 172 (c) 176 (d) 152
  5. 5.What is the missing term in the AP 3, ?, 15, 21, 27? (a) 10 (b) 15 (c) 9 (d) 8
  6. 6.What is the 34th term of the AP 10, 18, 26, 34, …? (a) 264 (b) 274 (c) 282 (d) 272
  7. 7.What is the sum of the first 6 terms of the AP 6, 7, 8, …? (a) 51 (b) 54 (c) 11 (d) 102
  8. 8.What is the missing term in the AP 4, 10, ?, 22, 28? (a) 22 (b) 15 (c) 17 (d) 16
  9. 9.What is the missing term in the AP 3, ?, 9, 12, 15? (a) 6 (b) 9 (c) 5 (d) 7
  10. 10.What is the 26th term of the AP 19, 27, 35, 43, …? (a) 200 (b) 208 (c) 219 (d) 227
  11. 11.What is the sum of the first 6 odd numbers (1 + 3 + 5 + …)? (a) 36 (b) 11 (c) 21 (d) 42
  12. 12.What is the 31st term of the AP 6, 12, 18, 24, …? (a) 187 (b) 186 (c) 180 (d) 192
  13. 13.What is the sum of the first 9 terms of the AP 5, 9, 13, …? (a) 189 (b) 37 (c) 207 (d) 378
  14. 14.What is the sum of the first 6 terms of the AP 3, 7, 11, …? (a) 23 (b) 78 (c) 90 (d) 156
  15. 15.What is the 10th term of the AP 5, 14, 23, 32, …? (a) 86 (b) 81 (c) 95 (d) 90
  16. 16.What is the sum of the first 5 terms of the AP 3, 6, 9, …? (a) 90 (b) 48 (c) 45 (d) 15
  17. 17.What is the missing term in the AP 19, 21, 23, ?, 27? (a) 27 (b) 25 (c) 26 (d) 24
  18. 18.What is the sum of all the whole numbers from 1 to 19? (a) 380 (b) 190 (c) 171 (d) 191
  19. 19.What is the missing term in the AP 19, 25, 31, ?, 43? (a) 38 (b) 43 (c) 37 (d) 36
  20. 20.What is the sum of the first 26 odd numbers (1 + 3 + 5 + …)? (a) 676 (b) 51 (c) 702 (d) 351
  21. 21.What is the sum of the first 8 terms of the AP 10, 14, 18, …? (a) 208 (b) 38 (c) 192 (d) 384
  22. 22.What is the 31st term of the AP 2, 4, 6, 8, …? (a) 62 (b) 60 (c) 64 (d) 63
  23. 23.What is the sum of all the whole numbers from 1 to 89? (a) 8010 (b) 4005 (c) 3916 (d) 4006
  24. 24.What is the 30th term of the AP 10, 18, 26, 34, …? (a) 240 (b) 250 (c) 232 (d) 242
  25. 25.What is the sum of the first 10 terms of the AP 9, 15, 21, …? (a) 720 (b) 360 (c) 63 (d) 390
  26. 26.What is the sum of all the whole numbers from 1 to 57? (a) 1596 (b) 3306 (c) 1654 (d) 1653
  27. 27.What is the missing term in the AP 13, 20, ?, 34, 41? (a) 26 (b) 27 (c) 34 (d) 28
  28. 28.What is the missing term in the AP 4, 6, 8, ?, 12? (a) 11 (b) 9 (c) 10 (d) 12
  29. 29.What is the 34th term of the AP 14, 22, 30, 38, …? (a) 272 (b) 278 (c) 286 (d) 264
  30. 30.What is the sum of the first 10 terms of the AP 2, 3, 4, …? (a) 70 (b) 130 (c) 65 (d) 11
  31. 31.What is the missing term in the AP 11, 15, 19, ?, 27? (a) 22 (b) 27 (c) 23 (d) 24
  32. 32.What is the sum of the first 7 terms of the AP 2, 4, 6, …? (a) 14 (b) 112 (c) 63 (d) 56
  33. 33.What is the 37th term of the AP 11, 18, 25, 32, …? (a) 263 (b) 259 (c) 270 (d) 252
  34. 34.What is the 34th term of the AP 4, 11, 18, 25, …? (a) 242 (b) 231 (c) 238 (d) 235
  35. 35.What is the 24th term of the AP 16, 25, 34, 43, …? (a) 207 (b) 216 (c) 232 (d) 223
  36. 36.What is the 10th term of the AP 10, 18, 26, 34, …? (a) 80 (b) 72 (c) 90 (d) 82
  37. 37.What is the 31st term of the AP 4, 9, 14, 19, …? (a) 150 (b) 154 (c) 155 (d) 159
  38. 38.What is the sum of the first 8 terms of the AP 1, 6, 11, …? (a) 148 (b) 168 (c) 296 (d) 36
  39. 39.What is the 36th term of the AP 9, 13, 17, 21, …? (a) 153 (b) 144 (c) 149 (d) 140
  40. 40.What is the sum of all the whole numbers from 1 to 97? (a) 4753 (b) 4754 (c) 4656 (d) 9506

Answer key

  1. 264
  2. 34th
  3. 305
  4. 172
  5. 9
  6. 274
  7. 51
  8. 16
  9. 6
  10. 219
  11. 36
  12. 186
  13. 189
  14. 78
  15. 86
  16. 45
  17. 25
  18. 190
  19. 37
  20. 676
  21. 192
  22. 62
  23. 4005
  24. 242
  25. 360
  26. 1653
  27. 27
  28. 10
  29. 278
  30. 65
  31. 23
  32. 56
  33. 263
  34. 235
  35. 223
  36. 82
  37. 154
  38. 148
  39. 149
  40. 4753

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