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Arithmetic Progression Worksheet for Olympiad

Maths Olympiad topic 29: Sequences and AP · Set 822 · 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 5 odd numbers (1 + 3 + 5 + …)? (a) 15 (b) 30 (c) 25 (d) 9
  2. 2.What is the sum of the first 11 terms of the AP 2, 3, 4, …? (a) 154 (b) 78 (c) 12 (d) 77
  3. 3.What is the 37th term of the AP 16, 20, 24, 28, …? (a) 148 (b) 160 (c) 164 (d) 144
  4. 4.What is the sum of the first 8 odd numbers (1 + 3 + 5 + …)? (a) 72 (b) 36 (c) 64 (d) 15
  5. 5.What is the sum of the first 8 terms of the AP 2, 7, 12, …? (a) 176 (b) 312 (c) 156 (d) 37
  6. 6.What is the 16th term of the AP 9, 11, 13, 15, …? (a) 39 (b) 30 (c) 41 (d) 32
  7. 7.What is the sum of the first 29 odd numbers (1 + 3 + 5 + …)? (a) 841 (b) 870 (c) 435 (d) 57
  8. 8.What is the sum of the first 21 odd numbers (1 + 3 + 5 + …)? (a) 231 (b) 441 (c) 41 (d) 462
  9. 9.What is the sum of the first 5 terms of the AP 4, 5, 6, …? (a) 31 (b) 8 (c) 60 (d) 30
  10. 10.What is the sum of all the whole numbers from 1 to 14? (a) 91 (b) 98 (c) 210 (d) 105
  11. 11.What is the 14th term of the AP 20, 29, 38, 47, …? (a) 146 (b) 117 (c) 137 (d) 126
  12. 12.What is the missing term in the AP 3, 11, ?, 27, 35? (a) 18 (b) 20 (c) 19 (d) 27
  13. 13.What is the 33rd term of the AP 19, 28, 37, 46, …? (a) 288 (b) 307 (c) 316 (d) 297
  14. 14.What is the sum of all the whole numbers from 1 to 32? (a) 496 (b) 528 (c) 512 (d) 1056
  15. 15.What is the 25th term of the AP 13, 15, 17, 19, …? (a) 50 (b) 48 (c) 61 (d) 63
  16. 16.What is the 30th term of the AP 3, 12, 21, 30, …? (a) 270 (b) 261 (c) 264 (d) 273
  17. 17.What is the missing term in the AP 16, ?, 24, 28, 32? (a) 19 (b) 24 (c) 21 (d) 20
  18. 18.Which term of the AP 7, 16, 25, 34, … is 142? (a) 15th (b) 17th (c) 16th (d) 18th
  19. 19.What is the sum of all the whole numbers from 1 to 86? (a) 7482 (b) 3698 (c) 3741 (d) 3655
  20. 20.What is the missing term in the AP 2, 5, ?, 11, 14? (a) 7 (b) 8 (c) 9 (d) 11
  21. 21.What is the 22nd term of the AP 9, 14, 19, 24, …? (a) 119 (b) 110 (c) 114 (d) 105
  22. 22.What is the sum of the first 10 terms of the AP 2, 4, 6, …? (a) 220 (b) 120 (c) 20 (d) 110
  23. 23.Which term of the AP 16, 24, 32, 40, … is 248? (a) 32nd (b) 31st (c) 29th (d) 30th
  24. 24.What is the sum of the first 10 odd numbers (1 + 3 + 5 + …)? (a) 19 (b) 55 (c) 110 (d) 100
  25. 25.What is the 24th term of the AP 3, 12, 21, 30, …? (a) 219 (b) 207 (c) 216 (d) 210
  26. 26.What is the 29th term of the AP 12, 20, 28, 36, …? (a) 232 (b) 236 (c) 244 (d) 224
  27. 27.What is the sum of the first 11 terms of the AP 8, 13, 18, …? (a) 363 (b) 726 (c) 368 (d) 58
  28. 28.Which term of the AP 13, 20, 27, 34, … is 223? (a) 32nd (b) 33rd (c) 30th (d) 31st
  29. 29.What is the sum of all the whole numbers from 1 to 97? (a) 9506 (b) 4754 (c) 4753 (d) 4656
  30. 30.What is the sum of all the whole numbers from 1 to 79? (a) 3161 (b) 6320 (c) 3160 (d) 3081
  31. 31.What is the sum of all the whole numbers from 1 to 56? (a) 1540 (b) 1568 (c) 3192 (d) 1596
  32. 32.What is the 12th term of the AP 6, 9, 12, 15, …? (a) 42 (b) 39 (c) 36 (d) 33
  33. 33.What is the 38th term of the AP 16, 21, 26, 31, …? (a) 206 (b) 190 (c) 185 (d) 201
  34. 34.What is the sum of the first 28 odd numbers (1 + 3 + 5 + …)? (a) 406 (b) 55 (c) 784 (d) 812
  35. 35.What is the 18th term of the AP 11, 20, 29, 38, …? (a) 164 (b) 173 (c) 153 (d) 162
  36. 36.What is the sum of the first 11 terms of the AP 6, 7, 8, …? (a) 121 (b) 242 (c) 16 (d) 122
  37. 37.What is the sum of the first 7 terms of the AP 3, 5, 7, …? (a) 15 (b) 70 (c) 63 (d) 126
  38. 38.What is the sum of the first 9 terms of the AP 9, 10, 11, …? (a) 234 (b) 117 (c) 118 (d) 17
  39. 39.What is the sum of the first 5 terms of the AP 1, 4, 7, …? (a) 70 (b) 35 (c) 38 (d) 13
  40. 40.Which term of the AP 5, 9, 13, 17, … is 153? (a) 37th (b) 40th (c) 39th (d) 38th

Answer key

  1. 25
  2. 77
  3. 160
  4. 64
  5. 156
  6. 39
  7. 841
  8. 441
  9. 30
  10. 105
  11. 137
  12. 19
  13. 307
  14. 528
  15. 61
  16. 264
  17. 20
  18. 16th
  19. 3741
  20. 8
  21. 114
  22. 110
  23. 30th
  24. 100
  25. 210
  26. 236
  27. 363
  28. 31st
  29. 4753
  30. 3160
  31. 1596
  32. 39
  33. 201
  34. 784
  35. 164
  36. 121
  37. 63
  38. 117
  39. 35
  40. 38th

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