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Arithmetic Progression Worksheet for Olympiad

Maths Olympiad topic 29: Sequences and AP · Set 926 · 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 17 odd numbers (1 + 3 + 5 + …)? (a) 153 (b) 289 (c) 33 (d) 306
  2. 2.What is the 14th term of the AP 3, 10, 17, 24, …? (a) 94 (b) 98 (c) 91 (d) 101
  3. 3.What is the sum of all the whole numbers from 1 to 30? (a) 930 (b) 450 (c) 465 (d) 435
  4. 4.What is the sum of all the whole numbers from 1 to 34? (a) 595 (b) 561 (c) 578 (d) 1190
  5. 5.What is the sum of the first 10 terms of the AP 2, 4, 6, …? (a) 220 (b) 20 (c) 110 (d) 120
  6. 6.What is the sum of the first 6 terms of the AP 9, 10, 11, …? (a) 138 (b) 72 (c) 14 (d) 69
  7. 7.What is the sum of the first 10 terms of the AP 10, 14, 18, …? (a) 46 (b) 560 (c) 280 (d) 300
  8. 8.What is the sum of all the whole numbers from 1 to 67? (a) 2211 (b) 2279 (c) 4556 (d) 2278
  9. 9.What is the sum of the first 9 terms of the AP 5, 10, 15, …? (a) 225 (b) 450 (c) 45 (d) 230
  10. 10.What is the missing term in the AP 10, ?, 14, 16, 18? (a) 13 (b) 11 (c) 12 (d) 14
  11. 11.What is the sum of the first 6 terms of the AP 2, 3, 4, …? (a) 7 (b) 27 (c) 54 (d) 30
  12. 12.What is the sum of the first 9 terms of the AP 7, 11, 15, …? (a) 39 (b) 414 (c) 207 (d) 225
  13. 13.What is the sum of the first 8 terms of the AP 6, 10, 14, …? (a) 320 (b) 176 (c) 160 (d) 34
  14. 14.What is the sum of all the whole numbers from 1 to 17? (a) 154 (b) 306 (c) 153 (d) 136
  15. 15.What is the sum of all the whole numbers from 1 to 76? (a) 2850 (b) 2888 (c) 2926 (d) 5852
  16. 16.What is the 22nd term of the AP 18, 20, 22, 24, …? (a) 42 (b) 62 (c) 60 (d) 44
  17. 17.What is the sum of the first 14 odd numbers (1 + 3 + 5 + …)? (a) 210 (b) 196 (c) 27 (d) 105
  18. 18.What is the sum of all the whole numbers from 1 to 85? (a) 3570 (b) 3656 (c) 3655 (d) 7310
  19. 19.What is the missing term in the AP 2, 7, ?, 17, 22? (a) 17 (b) 12 (c) 13 (d) 11
  20. 20.What is the sum of the first 12 terms of the AP 2, 3, 4, …? (a) 96 (b) 13 (c) 180 (d) 90
  21. 21.What is the sum of all the whole numbers from 1 to 77? (a) 2926 (b) 6006 (c) 3004 (d) 3003
  22. 22.What is the missing term in the AP 15, ?, 27, 33, 39? (a) 21 (b) 27 (c) 20 (d) 22
  23. 23.What is the 26th term of the AP 9, 16, 23, 30, …? (a) 184 (b) 191 (c) 175 (d) 182
  24. 24.What is the 19th term of the AP 7, 13, 19, 25, …? (a) 108 (b) 114 (c) 121 (d) 115
  25. 25.Which term of the AP 12, 14, 16, 18, … is 88? (a) 39th (b) 40th (c) 44th (d) 38th
  26. 26.What is the 40th term of the AP 7, 16, 25, 34, …? (a) 360 (b) 358 (c) 351 (d) 367
  27. 27.What is the missing term in the AP 4, 11, 18, ?, 32? (a) 25 (b) 24 (c) 32 (d) 26
  28. 28.What is the sum of the first 12 terms of the AP 6, 8, 10, …? (a) 408 (b) 204 (c) 28 (d) 216
  29. 29.What is the sum of all the whole numbers from 1 to 63? (a) 2017 (b) 1953 (c) 4032 (d) 2016
  30. 30.What is the 38th term of the AP 1, 9, 17, 25, …? (a) 296 (b) 304 (c) 297 (d) 305
  31. 31.Which term of the AP 11, 13, 15, 17, … is 73? (a) 31st (b) 33rd (c) 34th (d) 32nd
  32. 32.What is the sum of the first 6 terms of the AP 5, 7, 9, …? (a) 120 (b) 60 (c) 66 (d) 15
  33. 33.What is the 29th term of the AP 20, 27, 34, 41, …? (a) 196 (b) 223 (c) 203 (d) 216
  34. 34.What is the sum of all the whole numbers from 1 to 64? (a) 4160 (b) 2080 (c) 2016 (d) 2048
  35. 35.What is the sum of the first 8 terms of the AP 3, 9, 15, …? (a) 216 (b) 192 (c) 384 (d) 45
  36. 36.What is the sum of the first 12 terms of the AP 1, 2, 3, …? (a) 12 (b) 78 (c) 84 (d) 156
  37. 37.What is the missing term in the AP 15, ?, 23, 27, 31? (a) 19 (b) 18 (c) 20 (d) 23
  38. 38.What is the sum of all the whole numbers from 1 to 43? (a) 1892 (b) 947 (c) 903 (d) 946
  39. 39.What is the missing term in the AP 4, ?, 22, 31, 40? (a) 14 (b) 12 (c) 22 (d) 13
  40. 40.What is the sum of all the whole numbers from 1 to 32? (a) 512 (b) 496 (c) 528 (d) 1056

Answer key

  1. 289
  2. 94
  3. 465
  4. 595
  5. 110
  6. 69
  7. 280
  8. 2278
  9. 225
  10. 12
  11. 27
  12. 207
  13. 160
  14. 153
  15. 2926
  16. 60
  17. 196
  18. 3655
  19. 12
  20. 90
  21. 3003
  22. 21
  23. 184
  24. 115
  25. 39th
  26. 358
  27. 25
  28. 204
  29. 2016
  30. 297
  31. 32nd
  32. 60
  33. 216
  34. 2080
  35. 192
  36. 78
  37. 19
  38. 946
  39. 13
  40. 528

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