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Arithmetic Progression Worksheet for Olympiad

Maths Olympiad topic 29: Sequences and AP · Set 329 · 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 all the whole numbers from 1 to 52? (a) 1326 (b) 1352 (c) 1378 (d) 2756
  2. 2.What is the 13th term of the AP 6, 10, 14, 18, …? (a) 48 (b) 52 (c) 58 (d) 54
  3. 3.What is the sum of the first 9 terms of the AP 8, 10, 12, …? (a) 153 (b) 24 (c) 288 (d) 144
  4. 4.What is the sum of all the whole numbers from 1 to 20? (a) 210 (b) 200 (c) 190 (d) 420
  5. 5.What is the 37th term of the AP 6, 8, 10, 12, …? (a) 80 (b) 74 (c) 72 (d) 78
  6. 6.What is the sum of the first 12 terms of the AP 1, 7, 13, …? (a) 67 (b) 444 (c) 408 (d) 816
  7. 7.What is the 35th term of the AP 16, 23, 30, 37, …? (a) 245 (b) 238 (c) 261 (d) 254
  8. 8.What is the missing term in the AP 1, 10, 19, ?, 37? (a) 29 (b) 27 (c) 37 (d) 28
  9. 9.What is the 15th term of the AP 10, 12, 14, 16, …? (a) 38 (b) 40 (c) 28 (d) 30
  10. 10.What is the sum of the first 8 terms of the AP 3, 8, 13, …? (a) 328 (b) 38 (c) 164 (d) 184
  11. 11.What is the 16th term of the AP 16, 19, 22, 25, …? (a) 45 (b) 61 (c) 64 (d) 48
  12. 12.What is the sum of the first 8 terms of the AP 9, 10, 11, …? (a) 100 (b) 200 (c) 16 (d) 104
  13. 13.Which term of the AP 18, 24, 30, 36, … is 168? (a) 28th (b) 25th (c) 27th (d) 26th
  14. 14.What is the 40th term of the AP 13, 21, 29, 37, …? (a) 325 (b) 312 (c) 320 (d) 333
  15. 15.What is the sum of the first 12 terms of the AP 3, 4, 5, …? (a) 204 (b) 102 (c) 108 (d) 14
  16. 16.What is the sum of all the whole numbers from 1 to 74? (a) 2738 (b) 5550 (c) 2701 (d) 2775
  17. 17.What is the sum of all the whole numbers from 1 to 96? (a) 4608 (b) 4560 (c) 4656 (d) 9312
  18. 18.What is the sum of the first 6 terms of the AP 10, 12, 14, …? (a) 96 (b) 20 (c) 90 (d) 180
  19. 19.What is the sum of the first 12 terms of the AP 9, 10, 11, …? (a) 348 (b) 180 (c) 20 (d) 174
  20. 20.What is the 35th term of the AP 3, 6, 9, 12, …? (a) 108 (b) 105 (c) 106 (d) 102
  21. 21.What is the 36th term of the AP 10, 17, 24, 31, …? (a) 255 (b) 245 (c) 252 (d) 262
  22. 22.What is the sum of the first 10 terms of the AP 10, 12, 14, …? (a) 190 (b) 28 (c) 380 (d) 200
  23. 23.What is the sum of the first 5 terms of the AP 2, 8, 14, …? (a) 70 (b) 85 (c) 26 (d) 140
  24. 24.What is the sum of the first 9 terms of the AP 10, 14, 18, …? (a) 468 (b) 252 (c) 42 (d) 234
  25. 25.What is the 19th term of the AP 2, 8, 14, 20, …? (a) 116 (b) 114 (c) 110 (d) 108
  26. 26.What is the missing term in the AP 13, 15, 17, ?, 21? (a) 18 (b) 21 (c) 20 (d) 19
  27. 27.What is the sum of the first 11 terms of the AP 10, 11, 12, …? (a) 330 (b) 20 (c) 165 (d) 166
  28. 28.What is the 26th term of the AP 17, 25, 33, 41, …? (a) 225 (b) 208 (c) 217 (d) 200
  29. 29.What is the 29th term of the AP 2, 5, 8, 11, …? (a) 89 (b) 84 (c) 87 (d) 86
  30. 30.What is the 14th term of the AP 2, 5, 8, 11, …? (a) 42 (b) 44 (c) 41 (d) 39
  31. 31.What is the missing term in the AP 6, ?, 24, 33, 42? (a) 15 (b) 14 (c) 16 (d) 24
  32. 32.What is the sum of the first 5 terms of the AP 3, 7, 11, …? (a) 65 (b) 19 (c) 55 (d) 110
  33. 33.What is the 31st term of the AP 11, 18, 25, 32, …? (a) 228 (b) 217 (c) 221 (d) 210
  34. 34.What is the missing term in the AP 5, ?, 23, 32, 41? (a) 23 (b) 13 (c) 15 (d) 14
  35. 35.What is the 15th term of the AP 6, 12, 18, 24, …? (a) 90 (b) 96 (c) 91 (d) 84
  36. 36.What is the sum of the first 10 terms of the AP 1, 5, 9, …? (a) 380 (b) 190 (c) 210 (d) 37
  37. 37.What is the sum of all the whole numbers from 1 to 63? (a) 4032 (b) 1953 (c) 2016 (d) 2017
  38. 38.What is the sum of all the whole numbers from 1 to 68? (a) 2278 (b) 2312 (c) 4692 (d) 2346
  39. 39.What is the missing term in the AP 3, 7, 11, ?, 19? (a) 14 (b) 19 (c) 16 (d) 15
  40. 40.What is the sum of the first 7 terms of the AP 9, 10, 11, …? (a) 85 (b) 168 (c) 84 (d) 15

Answer key

  1. 1378
  2. 54
  3. 144
  4. 210
  5. 78
  6. 408
  7. 254
  8. 28
  9. 38
  10. 164
  11. 61
  12. 100
  13. 26th
  14. 325
  15. 102
  16. 2775
  17. 4656
  18. 90
  19. 174
  20. 105
  21. 255
  22. 190
  23. 70
  24. 234
  25. 110
  26. 19
  27. 165
  28. 217
  29. 86
  30. 41
  31. 15
  32. 55
  33. 221
  34. 14
  35. 90
  36. 190
  37. 2016
  38. 2346
  39. 15
  40. 84

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