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Arithmetic Progression Worksheet for Olympiad

Maths Olympiad topic 29: Sequences and AP · Set 997 · 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 11th term of the AP 19, 24, 29, 34, …? (a) 69 (b) 50 (c) 55 (d) 74
  2. 2.What is the sum of all the whole numbers from 1 to 43? (a) 903 (b) 946 (c) 1892 (d) 947
  3. 3.What is the 18th term of the AP 17, 19, 21, 23, …? (a) 34 (b) 51 (c) 36 (d) 53
  4. 4.What is the 32nd term of the AP 9, 12, 15, 18, …? (a) 93 (b) 105 (c) 102 (d) 96
  5. 5.What is the missing term in the AP 2, ?, 10, 14, 18? (a) 5 (b) 6 (c) 10 (d) 7
  6. 6.What is the sum of the first 10 terms of the AP 5, 6, 7, …? (a) 100 (b) 190 (c) 95 (d) 14
  7. 7.What is the sum of the first 10 terms of the AP 8, 10, 12, …? (a) 26 (b) 180 (c) 340 (d) 170
  8. 8.What is the sum of the first 9 terms of the AP 2, 8, 14, …? (a) 234 (b) 468 (c) 261 (d) 50
  9. 9.What is the 16th term of the AP 12, 20, 28, 36, …? (a) 128 (b) 140 (c) 132 (d) 120
  10. 10.What is the 28th term of the AP 11, 20, 29, 38, …? (a) 243 (b) 252 (c) 263 (d) 254
  11. 11.What is the 19th term of the AP 13, 15, 17, 19, …? (a) 51 (b) 49 (c) 38 (d) 36
  12. 12.What is the missing term in the AP 9, 13, 17, ?, 25? (a) 25 (b) 22 (c) 20 (d) 21
  13. 13.What is the sum of the first 30 odd numbers (1 + 3 + 5 + …)? (a) 930 (b) 900 (c) 465 (d) 59
  14. 14.What is the 12th term of the AP 1, 10, 19, 28, …? (a) 99 (b) 109 (c) 108 (d) 100
  15. 15.What is the sum of the first 7 terms of the AP 7, 9, 11, …? (a) 91 (b) 182 (c) 98 (d) 19
  16. 16.What is the sum of the first 11 terms of the AP 6, 12, 18, …? (a) 396 (b) 66 (c) 429 (d) 792
  17. 17.What is the sum of all the whole numbers from 1 to 29? (a) 435 (b) 870 (c) 436 (d) 406
  18. 18.What is the 20th term of the AP 2, 5, 8, 11, …? (a) 60 (b) 57 (c) 59 (d) 62
  19. 19.What is the missing term in the AP 5, ?, 15, 20, 25? (a) 15 (b) 11 (c) 9 (d) 10
  20. 20.What is the sum of the first 10 terms of the AP 8, 9, 10, …? (a) 130 (b) 17 (c) 125 (d) 250
  21. 21.What is the sum of the first 8 terms of the AP 2, 4, 6, …? (a) 16 (b) 144 (c) 80 (d) 72
  22. 22.What is the 29th term of the AP 1, 8, 15, 22, …? (a) 204 (b) 203 (c) 196 (d) 197
  23. 23.What is the sum of the first 11 terms of the AP 2, 6, 10, …? (a) 264 (b) 242 (c) 484 (d) 42
  24. 24.What is the 27th term of the AP 18, 25, 32, 39, …? (a) 189 (b) 200 (c) 182 (d) 207
  25. 25.What is the 30th term of the AP 17, 26, 35, 44, …? (a) 287 (b) 270 (c) 278 (d) 261
  26. 26.What is the 33rd term of the AP 17, 26, 35, 44, …? (a) 288 (b) 314 (c) 305 (d) 297
  27. 27.What is the sum of the first 18 odd numbers (1 + 3 + 5 + …)? (a) 171 (b) 35 (c) 324 (d) 342
  28. 28.What is the 30th term of the AP 14, 18, 22, 26, …? (a) 134 (b) 130 (c) 116 (d) 120
  29. 29.What is the 15th term of the AP 15, 19, 23, 27, …? (a) 60 (b) 71 (c) 56 (d) 75
  30. 30.What is the sum of the first 29 odd numbers (1 + 3 + 5 + …)? (a) 870 (b) 57 (c) 435 (d) 841
  31. 31.What is the sum of all the whole numbers from 1 to 68? (a) 2346 (b) 2278 (c) 4692 (d) 2312
  32. 32.What is the sum of all the whole numbers from 1 to 21? (a) 231 (b) 462 (c) 232 (d) 210
  33. 33.What is the sum of all the whole numbers from 1 to 20? (a) 200 (b) 420 (c) 210 (d) 190
  34. 34.What is the missing term in the AP 4, 6, 8, ?, 12? (a) 12 (b) 9 (c) 11 (d) 10
  35. 35.What is the sum of the first 5 terms of the AP 1, 7, 13, …? (a) 80 (b) 25 (c) 130 (d) 65
  36. 36.What is the 15th term of the AP 6, 9, 12, 15, …? (a) 51 (b) 45 (c) 42 (d) 48
  37. 37.What is the missing term in the AP 13, 16, ?, 22, 25? (a) 19 (b) 22 (c) 18 (d) 20
  38. 38.What is the sum of all the whole numbers from 1 to 56? (a) 3192 (b) 1568 (c) 1540 (d) 1596
  39. 39.What is the sum of the first 14 odd numbers (1 + 3 + 5 + …)? (a) 105 (b) 27 (c) 210 (d) 196
  40. 40.What is the sum of all the whole numbers from 1 to 84? (a) 7140 (b) 3528 (c) 3570 (d) 3486

Answer key

  1. 69
  2. 946
  3. 51
  4. 102
  5. 6
  6. 95
  7. 170
  8. 234
  9. 132
  10. 254
  11. 49
  12. 21
  13. 900
  14. 100
  15. 91
  16. 396
  17. 435
  18. 59
  19. 10
  20. 125
  21. 72
  22. 197
  23. 242
  24. 200
  25. 278
  26. 305
  27. 324
  28. 130
  29. 71
  30. 841
  31. 2346
  32. 231
  33. 210
  34. 10
  35. 65
  36. 48
  37. 19
  38. 1596
  39. 196
  40. 3570

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