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Arithmetic Progression Worksheet for Olympiad

Maths Olympiad topic 29: Sequences and AP · Set 892 · 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 61? (a) 1891 (b) 3782 (c) 1892 (d) 1830
  2. 2.What is the sum of the first 10 terms of the AP 4, 6, 8, …? (a) 260 (b) 130 (c) 140 (d) 22
  3. 3.What is the sum of all the whole numbers from 1 to 97? (a) 9506 (b) 4754 (c) 4656 (d) 4753
  4. 4.What is the sum of the first 10 terms of the AP 4, 10, 16, …? (a) 58 (b) 620 (c) 310 (d) 340
  5. 5.Which term of the AP 6, 10, 14, 18, … is 154? (a) 37th (b) 38th (c) 39th (d) 40th
  6. 6.What is the 24th term of the AP 13, 21, 29, 37, …? (a) 197 (b) 205 (c) 192 (d) 184
  7. 7.What is the 35th term of the AP 10, 14, 18, 22, …? (a) 150 (b) 136 (c) 146 (d) 140
  8. 8.What is the sum of the first 7 terms of the AP 3, 7, 11, …? (a) 105 (b) 119 (c) 27 (d) 210
  9. 9.What is the 34th term of the AP 14, 20, 26, 32, …? (a) 198 (b) 218 (c) 204 (d) 212
  10. 10.What is the 39th term of the AP 19, 22, 25, 28, …? (a) 114 (b) 117 (c) 136 (d) 133
  11. 11.What is the sum of all the whole numbers from 1 to 35? (a) 631 (b) 1260 (c) 630 (d) 595
  12. 12.What is the 38th term of the AP 5, 8, 11, 14, …? (a) 116 (b) 111 (c) 114 (d) 119
  13. 13.What is the sum of the first 27 odd numbers (1 + 3 + 5 + …)? (a) 756 (b) 53 (c) 378 (d) 729
  14. 14.What is the sum of the first 24 odd numbers (1 + 3 + 5 + …)? (a) 300 (b) 576 (c) 600 (d) 47
  15. 15.What is the 35th term of the AP 3, 12, 21, 30, …? (a) 318 (b) 315 (c) 306 (d) 309
  16. 16.What is the 20th term of the AP 20, 28, 36, 44, …? (a) 180 (b) 172 (c) 160 (d) 152
  17. 17.Which term of the AP 12, 18, 24, 30, … is 66? (a) 9th (b) 12th (c) 11th (d) 10th
  18. 18.What is the sum of the first 5 terms of the AP 4, 7, 10, …? (a) 53 (b) 16 (c) 100 (d) 50
  19. 19.What is the sum of the first 5 terms of the AP 7, 11, 15, …? (a) 85 (b) 75 (c) 23 (d) 150
  20. 20.What is the 31st term of the AP 19, 28, 37, 46, …? (a) 279 (b) 289 (c) 298 (d) 270
  21. 21.What is the sum of the first 12 terms of the AP 6, 10, 14, …? (a) 50 (b) 672 (c) 360 (d) 336
  22. 22.What is the missing term in the AP 3, ?, 9, 12, 15? (a) 7 (b) 5 (c) 6 (d) 9
  23. 23.What is the sum of all the whole numbers from 1 to 48? (a) 2352 (b) 1176 (c) 1152 (d) 1128
  24. 24.What is the sum of the first 6 terms of the AP 9, 14, 19, …? (a) 34 (b) 144 (c) 129 (d) 258
  25. 25.What is the missing term in the AP 14, 17, ?, 23, 26? (a) 21 (b) 23 (c) 19 (d) 20
  26. 26.What is the sum of all the whole numbers from 1 to 67? (a) 2278 (b) 4556 (c) 2279 (d) 2211
  27. 27.What is the sum of all the whole numbers from 1 to 96? (a) 9312 (b) 4608 (c) 4656 (d) 4560
  28. 28.What is the 30th term of the AP 12, 14, 16, 18, …? (a) 70 (b) 72 (c) 60 (d) 58
  29. 29.What is the missing term in the AP 3, ?, 11, 15, 19? (a) 6 (b) 11 (c) 7 (d) 8
  30. 30.What is the sum of the first 8 terms of the AP 10, 13, 16, …? (a) 31 (b) 164 (c) 176 (d) 328
  31. 31.What is the sum of all the whole numbers from 1 to 17? (a) 153 (b) 306 (c) 136 (d) 154
  32. 32.What is the sum of all the whole numbers from 1 to 42? (a) 882 (b) 861 (c) 903 (d) 1806
  33. 33.What is the 18th term of the AP 15, 22, 29, 36, …? (a) 141 (b) 119 (c) 126 (d) 134
  34. 34.What is the 23rd term of the AP 17, 22, 27, 32, …? (a) 115 (b) 110 (c) 127 (d) 132
  35. 35.What is the sum of the first 6 terms of the AP 2, 6, 10, …? (a) 22 (b) 72 (c) 144 (d) 84
  36. 36.What is the 39th term of the AP 16, 24, 32, 40, …? (a) 312 (b) 320 (c) 304 (d) 328
  37. 37.What is the 40th term of the AP 3, 11, 19, 27, …? (a) 320 (b) 323 (c) 315 (d) 312
  38. 38.What is the 14th term of the AP 5, 7, 9, 11, …? (a) 33 (b) 26 (c) 28 (d) 31
  39. 39.What is the 38th term of the AP 10, 17, 24, 31, …? (a) 259 (b) 266 (c) 276 (d) 269
  40. 40.Which term of the AP 16, 19, 22, 25, … is 100? (a) 29th (b) 31st (c) 30th (d) 28th

Answer key

  1. 1891
  2. 130
  3. 4753
  4. 310
  5. 38th
  6. 197
  7. 146
  8. 105
  9. 212
  10. 133
  11. 630
  12. 116
  13. 729
  14. 576
  15. 309
  16. 172
  17. 10th
  18. 50
  19. 75
  20. 289
  21. 336
  22. 6
  23. 1176
  24. 129
  25. 20
  26. 2278
  27. 4656
  28. 70
  29. 7
  30. 164
  31. 153
  32. 903
  33. 134
  34. 127
  35. 72
  36. 320
  37. 315
  38. 31
  39. 269
  40. 29th

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