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Arithmetic Progression Worksheet for Olympiad

Maths Olympiad topic 29: Sequences and AP · Set 277 · 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 missing term in the AP 6, 13, ?, 27, 34? (a) 21 (b) 20 (c) 19 (d) 27
  2. 2.What is the 32nd term of the AP 2, 10, 18, 26, …? (a) 256 (b) 250 (c) 248 (d) 258
  3. 3.What is the sum of the first 8 terms of the AP 7, 12, 17, …? (a) 196 (b) 392 (c) 42 (d) 216
  4. 4.Which term of the AP 5, 12, 19, 26, … is 236? (a) 35th (b) 34th (c) 36th (d) 33rd
  5. 5.What is the 18th term of the AP 5, 11, 17, 23, …? (a) 113 (b) 108 (c) 102 (d) 107
  6. 6.What is the missing term in the AP 18, 23, ?, 33, 38? (a) 27 (b) 33 (c) 29 (d) 28
  7. 7.What is the 18th term of the AP 10, 15, 20, 25, …? (a) 90 (b) 85 (c) 100 (d) 95
  8. 8.What is the sum of all the whole numbers from 1 to 78? (a) 3081 (b) 3042 (c) 3003 (d) 6162
  9. 9.What is the 23rd term of the AP 7, 16, 25, 34, …? (a) 205 (b) 214 (c) 207 (d) 198
  10. 10.What is the 14th term of the AP 11, 18, 25, 32, …? (a) 91 (b) 102 (c) 98 (d) 109
  11. 11.What is the 34th term of the AP 15, 24, 33, 42, …? (a) 312 (b) 297 (c) 306 (d) 321
  12. 12.What is the sum of the first 12 terms of the AP 7, 9, 11, …? (a) 29 (b) 228 (c) 216 (d) 432
  13. 13.What is the sum of all the whole numbers from 1 to 17? (a) 153 (b) 306 (c) 154 (d) 136
  14. 14.What is the 13th term of the AP 20, 22, 24, 26, …? (a) 24 (b) 26 (c) 44 (d) 46
  15. 15.What is the sum of the first 9 terms of the AP 9, 13, 17, …? (a) 41 (b) 225 (c) 450 (d) 243
  16. 16.What is the sum of the first 11 terms of the AP 2, 3, 4, …? (a) 12 (b) 78 (c) 77 (d) 154
  17. 17.What is the sum of the first 6 odd numbers (1 + 3 + 5 + …)? (a) 42 (b) 11 (c) 21 (d) 36
  18. 18.What is the 39th term of the AP 17, 26, 35, 44, …? (a) 359 (b) 351 (c) 342 (d) 368
  19. 19.What is the sum of the first 9 terms of the AP 3, 7, 11, …? (a) 35 (b) 342 (c) 189 (d) 171
  20. 20.What is the sum of the first 11 terms of the AP 8, 12, 16, …? (a) 616 (b) 330 (c) 308 (d) 48
  21. 21.What is the sum of all the whole numbers from 1 to 59? (a) 1711 (b) 3540 (c) 1771 (d) 1770
  22. 22.What is the 37th term of the AP 20, 29, 38, 47, …? (a) 324 (b) 353 (c) 344 (d) 333
  23. 23.What is the sum of all the whole numbers from 1 to 96? (a) 4608 (b) 9312 (c) 4656 (d) 4560
  24. 24.What is the 35th term of the AP 11, 20, 29, 38, …? (a) 317 (b) 315 (c) 306 (d) 326
  25. 25.What is the sum of the first 12 terms of the AP 3, 6, 9, …? (a) 252 (b) 468 (c) 234 (d) 36
  26. 26.What is the sum of all the whole numbers from 1 to 49? (a) 2450 (b) 1176 (c) 1226 (d) 1225
  27. 27.What is the 35th term of the AP 12, 14, 16, 18, …? (a) 80 (b) 70 (c) 68 (d) 82
  28. 28.What is the 19th term of the AP 18, 27, 36, 45, …? (a) 171 (b) 180 (c) 189 (d) 162
  29. 29.What is the sum of all the whole numbers from 1 to 71? (a) 2557 (b) 2485 (c) 2556 (d) 5112
  30. 30.What is the sum of all the whole numbers from 1 to 91? (a) 4095 (b) 8372 (c) 4187 (d) 4186
  31. 31.What is the sum of the first 11 terms of the AP 6, 10, 14, …? (a) 572 (b) 46 (c) 286 (d) 308
  32. 32.What is the sum of all the whole numbers from 1 to 56? (a) 3192 (b) 1568 (c) 1596 (d) 1540
  33. 33.What is the sum of the first 5 terms of the AP 2, 6, 10, …? (a) 18 (b) 100 (c) 60 (d) 50
  34. 34.What is the sum of the first 8 terms of the AP 2, 7, 12, …? (a) 176 (b) 312 (c) 37 (d) 156
  35. 35.What is the missing term in the AP 5, 9, ?, 17, 21? (a) 12 (b) 14 (c) 13 (d) 17
  36. 36.What is the 35th term of the AP 20, 23, 26, 29, …? (a) 102 (b) 122 (c) 105 (d) 125
  37. 37.What is the sum of the first 29 odd numbers (1 + 3 + 5 + …)? (a) 870 (b) 57 (c) 841 (d) 435
  38. 38.What is the 36th term of the AP 14, 19, 24, 29, …? (a) 194 (b) 180 (c) 175 (d) 189
  39. 39.What is the sum of all the whole numbers from 1 to 84? (a) 7140 (b) 3486 (c) 3570 (d) 3528
  40. 40.What is the sum of the first 6 terms of the AP 10, 16, 22, …? (a) 300 (b) 150 (c) 168 (d) 40

Answer key

  1. 20
  2. 250
  3. 196
  4. 34th
  5. 107
  6. 28
  7. 95
  8. 3081
  9. 205
  10. 102
  11. 312
  12. 216
  13. 153
  14. 44
  15. 225
  16. 77
  17. 36
  18. 359
  19. 171
  20. 308
  21. 1770
  22. 344
  23. 4656
  24. 317
  25. 234
  26. 1225
  27. 80
  28. 180
  29. 2556
  30. 4186
  31. 286
  32. 1596
  33. 50
  34. 156
  35. 13
  36. 122
  37. 841
  38. 189
  39. 3570
  40. 150

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