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Arithmetic Progression Worksheet for Olympiad

Maths Olympiad topic 29: Sequences and AP · Set 902 · 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 64? (a) 4160 (b) 2080 (c) 2016 (d) 2048
  2. 2.Which term of the AP 7, 9, 11, 13, … is 37? (a) 18th (b) 17th (c) 16th (d) 15th
  3. 3.Which term of the AP 17, 20, 23, 26, … is 50? (a) 13th (b) 14th (c) 11th (d) 12th
  4. 4.What is the 21st term of the AP 15, 24, 33, 42, …? (a) 195 (b) 180 (c) 204 (d) 189
  5. 5.What is the missing term in the AP 5, 8, ?, 14, 17? (a) 14 (b) 11 (c) 12 (d) 10
  6. 6.What is the 33rd term of the AP 3, 5, 7, 9, …? (a) 66 (b) 64 (c) 69 (d) 67
  7. 7.What is the 32nd term of the AP 5, 13, 21, 29, …? (a) 261 (b) 256 (c) 253 (d) 248
  8. 8.What is the sum of all the whole numbers from 1 to 45? (a) 1036 (b) 990 (c) 1035 (d) 2070
  9. 9.What is the 28th term of the AP 7, 14, 21, 28, …? (a) 196 (b) 197 (c) 203 (d) 189
  10. 10.Which term of the AP 7, 9, 11, 13, … is 57? (a) 28th (b) 26th (c) 25th (d) 27th
  11. 11.What is the 22nd term of the AP 13, 15, 17, 19, …? (a) 44 (b) 57 (c) 55 (d) 42
  12. 12.What is the sum of the first 5 terms of the AP 1, 4, 7, …? (a) 38 (b) 70 (c) 13 (d) 35
  13. 13.What is the sum of the first 6 terms of the AP 5, 7, 9, …? (a) 15 (b) 66 (c) 120 (d) 60
  14. 14.What is the sum of the first 6 terms of the AP 10, 16, 22, …? (a) 300 (b) 168 (c) 150 (d) 40
  15. 15.What is the sum of all the whole numbers from 1 to 66? (a) 2178 (b) 4422 (c) 2145 (d) 2211
  16. 16.What is the sum of the first 9 terms of the AP 8, 9, 10, …? (a) 16 (b) 109 (c) 216 (d) 108
  17. 17.What is the sum of the first 7 odd numbers (1 + 3 + 5 + …)? (a) 13 (b) 49 (c) 56 (d) 28
  18. 18.What is the sum of all the whole numbers from 1 to 94? (a) 4418 (b) 4371 (c) 4465 (d) 8930
  19. 19.What is the 23rd term of the AP 12, 17, 22, 27, …? (a) 115 (b) 127 (c) 110 (d) 122
  20. 20.What is the missing term in the AP 18, ?, 34, 42, 50? (a) 27 (b) 34 (c) 26 (d) 25
  21. 21.What is the 38th term of the AP 1, 4, 7, 10, …? (a) 111 (b) 114 (c) 112 (d) 115
  22. 22.What is the sum of the first 7 terms of the AP 3, 5, 7, …? (a) 70 (b) 63 (c) 15 (d) 126
  23. 23.What is the missing term in the AP 19, 22, ?, 28, 31? (a) 28 (b) 24 (c) 25 (d) 26
  24. 24.What is the sum of all the whole numbers from 1 to 75? (a) 2850 (b) 5700 (c) 2775 (d) 2851
  25. 25.What is the missing term in the AP 14, 17, 20, ?, 26? (a) 24 (b) 22 (c) 23 (d) 26
  26. 26.What is the sum of the first 8 odd numbers (1 + 3 + 5 + …)? (a) 15 (b) 72 (c) 36 (d) 64
  27. 27.What is the 35th term of the AP 3, 6, 9, 12, …? (a) 106 (b) 108 (c) 102 (d) 105
  28. 28.What is the 30th term of the AP 8, 10, 12, 14, …? (a) 68 (b) 58 (c) 66 (d) 60
  29. 29.Which term of the AP 1, 3, 5, 7, … is 55? (a) 29th (b) 27th (c) 30th (d) 28th
  30. 30.What is the sum of the first 23 odd numbers (1 + 3 + 5 + …)? (a) 529 (b) 552 (c) 45 (d) 276
  31. 31.Which term of the AP 13, 22, 31, 40, … is 184? (a) 20th (b) 22nd (c) 21st (d) 19th
  32. 32.What is the sum of the first 12 terms of the AP 1, 6, 11, …? (a) 342 (b) 56 (c) 684 (d) 372
  33. 33.What is the 23rd term of the AP 8, 17, 26, 35, …? (a) 207 (b) 198 (c) 206 (d) 215
  34. 34.What is the sum of all the whole numbers from 1 to 25? (a) 650 (b) 300 (c) 325 (d) 326
  35. 35.What is the sum of all the whole numbers from 1 to 29? (a) 870 (b) 406 (c) 436 (d) 435
  36. 36.What is the missing term in the AP 19, 27, ?, 43, 51? (a) 35 (b) 36 (c) 43 (d) 34
  37. 37.Which term of the AP 8, 11, 14, 17, … is 113? (a) 35th (b) 36th (c) 37th (d) 38th
  38. 38.What is the 34th term of the AP 15, 20, 25, 30, …? (a) 165 (b) 185 (c) 170 (d) 180
  39. 39.What is the sum of all the whole numbers from 1 to 14? (a) 98 (b) 91 (c) 210 (d) 105
  40. 40.What is the 13th term of the AP 5, 14, 23, 32, …? (a) 117 (b) 113 (c) 122 (d) 108

Answer key

  1. 2080
  2. 16th
  3. 12th
  4. 195
  5. 11
  6. 67
  7. 253
  8. 1035
  9. 196
  10. 26th
  11. 55
  12. 35
  13. 60
  14. 150
  15. 2211
  16. 108
  17. 49
  18. 4465
  19. 122
  20. 26
  21. 112
  22. 63
  23. 25
  24. 2850
  25. 23
  26. 64
  27. 105
  28. 66
  29. 28th
  30. 529
  31. 20th
  32. 342
  33. 206
  34. 325
  35. 435
  36. 35
  37. 36th
  38. 180
  39. 105
  40. 113

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