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Arithmetic Progression Worksheet for Olympiad

Maths Olympiad topic 29: Sequences and AP · Set 96 · 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 terms of the AP 2, 4, 6, …? (a) 10 (b) 60 (c) 35 (d) 30
  2. 2.What is the missing term in the AP 19, 27, 35, ?, 51? (a) 51 (b) 43 (c) 44 (d) 42
  3. 3.What is the 36th term of the AP 15, 19, 23, 27, …? (a) 140 (b) 159 (c) 144 (d) 155
  4. 4.What is the sum of the first 9 terms of the AP 6, 7, 8, …? (a) 180 (b) 14 (c) 91 (d) 90
  5. 5.What is the sum of the first 12 terms of the AP 7, 8, 9, …? (a) 156 (b) 18 (c) 150 (d) 300
  6. 6.What is the 12th term of the AP 18, 27, 36, 45, …? (a) 126 (b) 108 (c) 117 (d) 99
  7. 7.What is the 20th term of the AP 12, 21, 30, 39, …? (a) 183 (b) 192 (c) 180 (d) 171
  8. 8.What is the sum of the first 24 odd numbers (1 + 3 + 5 + …)? (a) 300 (b) 47 (c) 600 (d) 576
  9. 9.What is the sum of all the whole numbers from 1 to 74? (a) 2775 (b) 2701 (c) 2738 (d) 5550
  10. 10.What is the missing term in the AP 2, ?, 16, 23, 30? (a) 8 (b) 9 (c) 16 (d) 10
  11. 11.What is the 37th term of the AP 5, 14, 23, 32, …? (a) 338 (b) 324 (c) 329 (d) 333
  12. 12.What is the missing term in the AP 7, 11, ?, 19, 23? (a) 14 (b) 16 (c) 19 (d) 15
  13. 13.Which term of the AP 10, 17, 24, 31, … is 129? (a) 20th (b) 17th (c) 18th (d) 19th
  14. 14.What is the missing term in the AP 9, 11, 13, ?, 17? (a) 17 (b) 16 (c) 14 (d) 15
  15. 15.What is the 29th term of the AP 14, 21, 28, 35, …? (a) 217 (b) 203 (c) 210 (d) 196
  16. 16.Which term of the AP 1, 6, 11, 16, … is 66? (a) 13th (b) 15th (c) 14th (d) 16th
  17. 17.Which term of the AP 8, 14, 20, 26, … is 134? (a) 24th (b) 22nd (c) 23rd (d) 21st
  18. 18.What is the 19th term of the AP 16, 23, 30, 37, …? (a) 133 (b) 126 (c) 149 (d) 142
  19. 19.What is the sum of the first 12 terms of the AP 10, 15, 20, …? (a) 65 (b) 450 (c) 900 (d) 480
  20. 20.What is the sum of the first 6 odd numbers (1 + 3 + 5 + …)? (a) 11 (b) 42 (c) 36 (d) 21
  21. 21.What is the 22nd term of the AP 18, 20, 22, 24, …? (a) 60 (b) 62 (c) 42 (d) 44
  22. 22.What is the sum of all the whole numbers from 1 to 88? (a) 7832 (b) 3916 (c) 3872 (d) 3828
  23. 23.What is the missing term in the AP 2, 11, 20, ?, 38? (a) 28 (b) 38 (c) 29 (d) 30
  24. 24.What is the sum of the first 8 terms of the AP 8, 11, 14, …? (a) 160 (b) 148 (c) 296 (d) 29
  25. 25.What is the 38th term of the AP 3, 8, 13, 18, …? (a) 185 (b) 188 (c) 190 (d) 193
  26. 26.What is the 23rd term of the AP 18, 25, 32, 39, …? (a) 154 (b) 172 (c) 179 (d) 161
  27. 27.What is the sum of all the whole numbers from 1 to 53? (a) 2862 (b) 1431 (c) 1432 (d) 1378
  28. 28.What is the 39th term of the AP 15, 23, 31, 39, …? (a) 327 (b) 312 (c) 319 (d) 304
  29. 29.What is the sum of all the whole numbers from 1 to 39? (a) 741 (b) 1560 (c) 780 (d) 781
  30. 30.What is the sum of the first 5 terms of the AP 2, 5, 8, …? (a) 43 (b) 40 (c) 14 (d) 80
  31. 31.What is the sum of the first 8 terms of the AP 6, 8, 10, …? (a) 208 (b) 104 (c) 112 (d) 20
  32. 32.What is the sum of the first 10 terms of the AP 10, 15, 20, …? (a) 55 (b) 350 (c) 650 (d) 325
  33. 33.What is the sum of the first 12 terms of the AP 3, 6, 9, …? (a) 36 (b) 252 (c) 234 (d) 468
  34. 34.What is the sum of the first 14 odd numbers (1 + 3 + 5 + …)? (a) 196 (b) 27 (c) 210 (d) 105
  35. 35.What is the sum of the first 6 terms of the AP 9, 15, 21, …? (a) 144 (b) 39 (c) 162 (d) 288
  36. 36.What is the sum of the first 10 terms of the AP 1, 6, 11, …? (a) 46 (b) 235 (c) 470 (d) 260
  37. 37.What is the sum of the first 11 terms of the AP 10, 11, 12, …? (a) 330 (b) 166 (c) 165 (d) 20
  38. 38.What is the 17th term of the AP 3, 8, 13, 18, …? (a) 80 (b) 83 (c) 85 (d) 88
  39. 39.What is the sum of the first 5 terms of the AP 7, 11, 15, …? (a) 150 (b) 75 (c) 85 (d) 23
  40. 40.Which term of the AP 7, 15, 23, 31, … is 231? (a) 29th (b) 30th (c) 28th (d) 31st

Answer key

  1. 30
  2. 43
  3. 155
  4. 90
  5. 150
  6. 117
  7. 183
  8. 576
  9. 2775
  10. 9
  11. 329
  12. 15
  13. 18th
  14. 15
  15. 210
  16. 14th
  17. 22nd
  18. 142
  19. 450
  20. 36
  21. 60
  22. 3916
  23. 29
  24. 148
  25. 188
  26. 172
  27. 1431
  28. 319
  29. 780
  30. 40
  31. 104
  32. 325
  33. 234
  34. 196
  35. 144
  36. 235
  37. 165
  38. 83
  39. 75
  40. 29th

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