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Arithmetic Progression Worksheet for Olympiad

Maths Olympiad topic 29: Sequences and AP · Set 462 · 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 77? (a) 6006 (b) 2926 (c) 3004 (d) 3003
  2. 2.What is the 12th term of the AP 19, 25, 31, 37, …? (a) 91 (b) 85 (c) 72 (d) 66
  3. 3.What is the sum of the first 12 terms of the AP 8, 12, 16, …? (a) 52 (b) 720 (c) 384 (d) 360
  4. 4.What is the missing term in the AP 13, ?, 25, 31, 37? (a) 25 (b) 18 (c) 20 (d) 19
  5. 5.What is the 39th term of the AP 16, 20, 24, 28, …? (a) 168 (b) 172 (c) 152 (d) 156
  6. 6.What is the sum of the first 8 terms of the AP 7, 12, 17, …? (a) 392 (b) 42 (c) 216 (d) 196
  7. 7.What is the 22nd term of the AP 4, 12, 20, 28, …? (a) 168 (b) 180 (c) 176 (d) 172
  8. 8.Which term of the AP 17, 19, 21, 23, … is 91? (a) 38th (b) 40th (c) 37th (d) 39th
  9. 9.Which term of the AP 10, 17, 24, 31, … is 164? (a) 22nd (b) 24th (c) 23rd (d) 25th
  10. 10.What is the 37th term of the AP 11, 14, 17, 20, …? (a) 111 (b) 119 (c) 108 (d) 122
  11. 11.What is the sum of the first 6 terms of the AP 3, 9, 15, …? (a) 33 (b) 126 (c) 216 (d) 108
  12. 12.What is the sum of all the whole numbers from 1 to 91? (a) 4186 (b) 4187 (c) 4095 (d) 8372
  13. 13.What is the sum of the first 7 terms of the AP 6, 9, 12, …? (a) 108 (b) 24 (c) 105 (d) 210
  14. 14.What is the 36th term of the AP 4, 8, 12, 16, …? (a) 148 (b) 145 (c) 140 (d) 144
  15. 15.What is the 12th term of the AP 19, 23, 27, 31, …? (a) 44 (b) 48 (c) 67 (d) 63
  16. 16.What is the sum of all the whole numbers from 1 to 59? (a) 1711 (b) 1770 (c) 1771 (d) 3540
  17. 17.What is the 30th term of the AP 13, 22, 31, 40, …? (a) 274 (b) 261 (c) 270 (d) 283
  18. 18.What is the sum of all the whole numbers from 1 to 32? (a) 528 (b) 512 (c) 1056 (d) 496
  19. 19.What is the missing term in the AP 12, ?, 16, 18, 20? (a) 13 (b) 15 (c) 16 (d) 14
  20. 20.What is the 18th term of the AP 10, 12, 14, 16, …? (a) 44 (b) 36 (c) 34 (d) 46
  21. 21.What is the sum of the first 11 terms of the AP 8, 11, 14, …? (a) 38 (b) 256 (c) 253 (d) 506
  22. 22.What is the sum of the first 10 terms of the AP 5, 11, 17, …? (a) 59 (b) 350 (c) 640 (d) 320
  23. 23.What is the sum of the first 10 terms of the AP 10, 12, 14, …? (a) 380 (b) 200 (c) 28 (d) 190
  24. 24.What is the sum of all the whole numbers from 1 to 17? (a) 153 (b) 136 (c) 154 (d) 306
  25. 25.What is the 25th term of the AP 19, 25, 31, 37, …? (a) 150 (b) 163 (c) 144 (d) 169
  26. 26.What is the 29th term of the AP 12, 16, 20, 24, …? (a) 116 (b) 124 (c) 128 (d) 112
  27. 27.What is the missing term in the AP 19, ?, 35, 43, 51? (a) 28 (b) 35 (c) 26 (d) 27
  28. 28.What is the 34th term of the AP 6, 8, 10, 12, …? (a) 66 (b) 72 (c) 68 (d) 74
  29. 29.Which term of the AP 4, 12, 20, 28, … is 156? (a) 22nd (b) 20th (c) 19th (d) 21st
  30. 30.What is the 34th term of the AP 4, 13, 22, 31, …? (a) 301 (b) 306 (c) 310 (d) 297
  31. 31.What is the sum of the first 25 odd numbers (1 + 3 + 5 + …)? (a) 650 (b) 325 (c) 49 (d) 625
  32. 32.What is the sum of the first 5 odd numbers (1 + 3 + 5 + …)? (a) 15 (b) 25 (c) 30 (d) 9
  33. 33.What is the missing term in the AP 19, 22, ?, 28, 31? (a) 24 (b) 26 (c) 25 (d) 28
  34. 34.What is the sum of the first 11 terms of the AP 2, 4, 6, …? (a) 264 (b) 143 (c) 22 (d) 132
  35. 35.What is the sum of all the whole numbers from 1 to 16? (a) 120 (b) 272 (c) 136 (d) 128
  36. 36.What is the sum of the first 6 terms of the AP 1, 5, 9, …? (a) 132 (b) 21 (c) 78 (d) 66
  37. 37.What is the sum of all the whole numbers from 1 to 57? (a) 3306 (b) 1654 (c) 1653 (d) 1596
  38. 38.What is the sum of all the whole numbers from 1 to 60? (a) 3660 (b) 1830 (c) 1770 (d) 1800
  39. 39.What is the 27th term of the AP 4, 12, 20, 28, …? (a) 208 (b) 216 (c) 220 (d) 212
  40. 40.What is the sum of all the whole numbers from 1 to 18? (a) 342 (b) 162 (c) 171 (d) 153

Answer key

  1. 3003
  2. 85
  3. 360
  4. 19
  5. 168
  6. 196
  7. 172
  8. 38th
  9. 23rd
  10. 119
  11. 108
  12. 4186
  13. 105
  14. 144
  15. 63
  16. 1770
  17. 274
  18. 528
  19. 14
  20. 44
  21. 253
  22. 320
  23. 190
  24. 153
  25. 163
  26. 124
  27. 27
  28. 72
  29. 20th
  30. 301
  31. 625
  32. 25
  33. 25
  34. 132
  35. 136
  36. 66
  37. 1653
  38. 1830
  39. 212
  40. 171

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