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Arithmetic Progression Worksheet for Olympiad

Maths Olympiad topic 29: Sequences and AP · Set 126 · 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 11 terms of the AP 6, 10, 14, …? (a) 572 (b) 286 (c) 308 (d) 46
  2. 2.Which term of the AP 10, 17, 24, 31, … is 255? (a) 37th (b) 35th (c) 38th (d) 36th
  3. 3.What is the 15th term of the AP 1, 7, 13, 19, …? (a) 85 (b) 84 (c) 91 (d) 90
  4. 4.What is the missing term in the AP 14, ?, 22, 26, 30? (a) 17 (b) 18 (c) 19 (d) 22
  5. 5.Which term of the AP 11, 20, 29, 38, … is 317? (a) 34th (b) 35th (c) 36th (d) 37th
  6. 6.Which term of the AP 4, 6, 8, 10, … is 74? (a) 36th (b) 37th (c) 38th (d) 35th
  7. 7.What is the sum of all the whole numbers from 1 to 37? (a) 703 (b) 666 (c) 1406 (d) 704
  8. 8.What is the sum of the first 5 odd numbers (1 + 3 + 5 + …)? (a) 30 (b) 25 (c) 9 (d) 15
  9. 9.What is the missing term in the AP 19, ?, 31, 37, 43? (a) 26 (b) 31 (c) 24 (d) 25
  10. 10.What is the 20th term of the AP 3, 10, 17, 24, …? (a) 143 (b) 136 (c) 133 (d) 140
  11. 11.What is the sum of the first 6 terms of the AP 3, 7, 11, …? (a) 23 (b) 156 (c) 90 (d) 78
  12. 12.What is the 11th term of the AP 2, 5, 8, 11, …? (a) 35 (b) 33 (c) 32 (d) 30
  13. 13.What is the 20th term of the AP 15, 19, 23, 27, …? (a) 80 (b) 95 (c) 91 (d) 76
  14. 14.What is the sum of all the whole numbers from 1 to 64? (a) 2080 (b) 4160 (c) 2016 (d) 2048
  15. 15.Which term of the AP 4, 9, 14, 19, … is 84? (a) 18th (b) 19th (c) 16th (d) 17th
  16. 16.Which term of the AP 17, 25, 33, 41, … is 89? (a) 12th (b) 10th (c) 9th (d) 11th
  17. 17.What is the 20th term of the AP 6, 10, 14, 18, …? (a) 80 (b) 86 (c) 76 (d) 82
  18. 18.What is the 27th term of the AP 16, 25, 34, 43, …? (a) 243 (b) 250 (c) 259 (d) 234
  19. 19.What is the 16th term of the AP 19, 24, 29, 34, …? (a) 94 (b) 99 (c) 75 (d) 80
  20. 20.What is the 28th term of the AP 1, 8, 15, 22, …? (a) 196 (b) 189 (c) 190 (d) 197
  21. 21.What is the sum of the first 10 terms of the AP 6, 10, 14, …? (a) 480 (b) 42 (c) 260 (d) 240
  22. 22.What is the 14th term of the AP 9, 12, 15, 18, …? (a) 42 (b) 39 (c) 48 (d) 51
  23. 23.What is the sum of the first 11 terms of the AP 10, 14, 18, …? (a) 660 (b) 330 (c) 352 (d) 50
  24. 24.What is the sum of all the whole numbers from 1 to 17? (a) 153 (b) 306 (c) 136 (d) 154
  25. 25.What is the 10th term of the AP 2, 8, 14, 20, …? (a) 54 (b) 56 (c) 62 (d) 60
  26. 26.What is the sum of the first 12 terms of the AP 8, 11, 14, …? (a) 588 (b) 294 (c) 41 (d) 312
  27. 27.What is the sum of all the whole numbers from 1 to 18? (a) 162 (b) 153 (c) 171 (d) 342
  28. 28.What is the sum of all the whole numbers from 1 to 90? (a) 4050 (b) 4095 (c) 8190 (d) 4005
  29. 29.What is the sum of the first 6 terms of the AP 1, 5, 9, …? (a) 132 (b) 21 (c) 78 (d) 66
  30. 30.What is the sum of the first 30 odd numbers (1 + 3 + 5 + …)? (a) 465 (b) 59 (c) 930 (d) 900
  31. 31.What is the sum of the first 9 terms of the AP 6, 11, 16, …? (a) 234 (b) 468 (c) 239 (d) 46
  32. 32.What is the sum of the first 5 terms of the AP 4, 7, 10, …? (a) 16 (b) 53 (c) 100 (d) 50
  33. 33.What is the missing term in the AP 6, 14, 22, ?, 38? (a) 30 (b) 31 (c) 29 (d) 38
  34. 34.What is the 33rd term of the AP 6, 12, 18, 24, …? (a) 199 (b) 204 (c) 192 (d) 198
  35. 35.What is the sum of all the whole numbers from 1 to 44? (a) 1980 (b) 946 (c) 990 (d) 968
  36. 36.What is the 24th term of the AP 19, 24, 29, 34, …? (a) 120 (b) 134 (c) 115 (d) 139
  37. 37.Which term of the AP 5, 9, 13, 17, … is 137? (a) 33rd (b) 34th (c) 35th (d) 36th
  38. 38.What is the 17th term of the AP 14, 22, 30, 38, …? (a) 136 (b) 150 (c) 128 (d) 142
  39. 39.What is the 23rd term of the AP 19, 22, 25, 28, …? (a) 66 (b) 88 (c) 85 (d) 69
  40. 40.What is the 40th term of the AP 19, 27, 35, 43, …? (a) 339 (b) 331 (c) 312 (d) 320

Answer key

  1. 286
  2. 36th
  3. 85
  4. 18
  5. 35th
  6. 36th
  7. 703
  8. 25
  9. 25
  10. 136
  11. 78
  12. 32
  13. 91
  14. 2080
  15. 17th
  16. 10th
  17. 82
  18. 250
  19. 94
  20. 190
  21. 240
  22. 48
  23. 330
  24. 153
  25. 56
  26. 294
  27. 171
  28. 4095
  29. 66
  30. 900
  31. 234
  32. 50
  33. 30
  34. 198
  35. 990
  36. 134
  37. 34th
  38. 142
  39. 85
  40. 331

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