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Arithmetic Progression Worksheet for Olympiad

Maths Olympiad topic 29: Sequences and AP · Set 350 · 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 73? (a) 2702 (b) 2628 (c) 5402 (d) 2701
  2. 2.What is the sum of all the whole numbers from 1 to 51? (a) 1275 (b) 1326 (c) 1327 (d) 2652
  3. 3.What is the 20th term of the AP 16, 19, 22, 25, …? (a) 57 (b) 76 (c) 73 (d) 60
  4. 4.What is the missing term in the AP 15, 21, 27, ?, 39? (a) 39 (b) 34 (c) 32 (d) 33
  5. 5.What is the 35th term of the AP 3, 6, 9, 12, …? (a) 102 (b) 105 (c) 106 (d) 108
  6. 6.What is the sum of the first 8 terms of the AP 3, 9, 15, …? (a) 45 (b) 216 (c) 384 (d) 192
  7. 7.What is the 24th term of the AP 6, 8, 10, 12, …? (a) 52 (b) 54 (c) 48 (d) 46
  8. 8.Which term of the AP 15, 19, 23, 27, … is 127? (a) 31st (b) 29th (c) 28th (d) 30th
  9. 9.Which term of the AP 3, 11, 19, 27, … is 283? (a) 35th (b) 38th (c) 36th (d) 37th
  10. 10.What is the 16th term of the AP 20, 27, 34, 41, …? (a) 112 (b) 132 (c) 105 (d) 125
  11. 11.What is the sum of the first 5 terms of the AP 3, 7, 11, …? (a) 110 (b) 65 (c) 55 (d) 19
  12. 12.What is the missing term in the AP 9, 12, ?, 18, 21? (a) 18 (b) 16 (c) 15 (d) 14
  13. 13.What is the sum of the first 26 odd numbers (1 + 3 + 5 + …)? (a) 51 (b) 351 (c) 702 (d) 676
  14. 14.What is the sum of all the whole numbers from 1 to 44? (a) 946 (b) 968 (c) 990 (d) 1980
  15. 15.What is the sum of the first 23 odd numbers (1 + 3 + 5 + …)? (a) 529 (b) 276 (c) 552 (d) 45
  16. 16.What is the 12th term of the AP 6, 9, 12, 15, …? (a) 42 (b) 33 (c) 36 (d) 39
  17. 17.What is the missing term in the AP 4, ?, 22, 31, 40? (a) 13 (b) 22 (c) 14 (d) 12
  18. 18.What is the sum of the first 12 terms of the AP 5, 6, 7, …? (a) 252 (b) 16 (c) 126 (d) 132
  19. 19.What is the sum of the first 5 terms of the AP 7, 8, 9, …? (a) 45 (b) 11 (c) 46 (d) 90
  20. 20.What is the 13th term of the AP 7, 14, 21, 28, …? (a) 92 (b) 98 (c) 91 (d) 84
  21. 21.What is the sum of the first 7 terms of the AP 10, 16, 22, …? (a) 46 (b) 392 (c) 196 (d) 217
  22. 22.What is the sum of the first 8 terms of the AP 10, 11, 12, …? (a) 17 (b) 108 (c) 216 (d) 112
  23. 23.What is the sum of the first 7 terms of the AP 10, 12, 14, …? (a) 112 (b) 119 (c) 22 (d) 224
  24. 24.What is the 36th term of the AP 12, 17, 22, 27, …? (a) 187 (b) 192 (c) 180 (d) 175
  25. 25.What is the sum of the first 16 odd numbers (1 + 3 + 5 + …)? (a) 256 (b) 31 (c) 272 (d) 136
  26. 26.What is the sum of the first 12 terms of the AP 2, 5, 8, …? (a) 35 (b) 444 (c) 222 (d) 240
  27. 27.What is the 13th term of the AP 12, 17, 22, 27, …? (a) 77 (b) 72 (c) 65 (d) 60
  28. 28.What is the 22nd term of the AP 11, 13, 15, 17, …? (a) 44 (b) 42 (c) 53 (d) 55
  29. 29.What is the missing term in the AP 17, ?, 33, 41, 49? (a) 33 (b) 26 (c) 25 (d) 24
  30. 30.What is the sum of the first 6 terms of the AP 2, 3, 4, …? (a) 30 (b) 7 (c) 27 (d) 54
  31. 31.What is the missing term in the AP 10, 19, 28, ?, 46? (a) 36 (b) 46 (c) 38 (d) 37
  32. 32.Which term of the AP 19, 22, 25, 28, … is 52? (a) 14th (b) 11th (c) 12th (d) 13th
  33. 33.What is the sum of all the whole numbers from 1 to 63? (a) 1953 (b) 2017 (c) 2016 (d) 4032
  34. 34.What is the 38th term of the AP 13, 19, 25, 31, …? (a) 241 (b) 235 (c) 228 (d) 222
  35. 35.What is the missing term in the AP 13, ?, 27, 34, 41? (a) 20 (b) 21 (c) 19 (d) 27
  36. 36.What is the 23rd term of the AP 7, 16, 25, 34, …? (a) 205 (b) 214 (c) 198 (d) 207
  37. 37.What is the sum of the first 8 terms of the AP 5, 11, 17, …? (a) 47 (b) 416 (c) 208 (d) 232
  38. 38.What is the missing term in the AP 12, ?, 26, 33, 40? (a) 20 (b) 19 (c) 26 (d) 18
  39. 39.What is the sum of all the whole numbers from 1 to 13? (a) 91 (b) 78 (c) 182 (d) 92
  40. 40.What is the 36th term of the AP 7, 13, 19, 25, …? (a) 216 (b) 223 (c) 217 (d) 210

Answer key

  1. 2701
  2. 1326
  3. 73
  4. 33
  5. 105
  6. 192
  7. 52
  8. 29th
  9. 36th
  10. 125
  11. 55
  12. 15
  13. 676
  14. 990
  15. 529
  16. 39
  17. 13
  18. 126
  19. 45
  20. 91
  21. 196
  22. 108
  23. 112
  24. 187
  25. 256
  26. 222
  27. 72
  28. 53
  29. 25
  30. 27
  31. 37
  32. 12th
  33. 2016
  34. 235
  35. 20
  36. 205
  37. 208
  38. 19
  39. 91
  40. 217

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