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Arithmetic Progression Worksheet for Olympiad

Maths Olympiad topic 29: Sequences and AP · Set 287 · 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 9 terms of the AP 1, 6, 11, …? (a) 194 (b) 189 (c) 378 (d) 41
  2. 2.Which term of the AP 4, 10, 16, 22, … is 232? (a) 41st (b) 38th (c) 39th (d) 40th
  3. 3.What is the 24th term of the AP 20, 27, 34, 41, …? (a) 181 (b) 188 (c) 168 (d) 161
  4. 4.What is the sum of all the whole numbers from 1 to 20? (a) 190 (b) 420 (c) 200 (d) 210
  5. 5.What is the sum of all the whole numbers from 1 to 81? (a) 6642 (b) 3240 (c) 3321 (d) 3322
  6. 6.What is the sum of the first 6 terms of the AP 3, 6, 9, …? (a) 18 (b) 63 (c) 72 (d) 126
  7. 7.What is the sum of the first 6 terms of the AP 5, 11, 17, …? (a) 240 (b) 35 (c) 120 (d) 138
  8. 8.What is the 10th term of the AP 2, 5, 8, 11, …? (a) 30 (b) 29 (c) 27 (d) 32
  9. 9.What is the sum of all the whole numbers from 1 to 66? (a) 2145 (b) 2211 (c) 4422 (d) 2178
  10. 10.What is the sum of the first 7 terms of the AP 10, 11, 12, …? (a) 182 (b) 92 (c) 16 (d) 91
  11. 11.What is the missing term in the AP 15, 21, 27, ?, 39? (a) 34 (b) 39 (c) 32 (d) 33
  12. 12.What is the 38th term of the AP 6, 13, 20, 27, …? (a) 265 (b) 266 (c) 272 (d) 259
  13. 13.What is the sum of all the whole numbers from 1 to 21? (a) 210 (b) 462 (c) 232 (d) 231
  14. 14.What is the 16th term of the AP 17, 23, 29, 35, …? (a) 96 (b) 90 (c) 113 (d) 107
  15. 15.What is the missing term in the AP 6, 13, ?, 27, 34? (a) 19 (b) 20 (c) 21 (d) 27
  16. 16.What is the 31st term of the AP 11, 14, 17, 20, …? (a) 104 (b) 101 (c) 93 (d) 90
  17. 17.What is the missing term in the AP 8, 10, ?, 14, 16? (a) 13 (b) 11 (c) 14 (d) 12
  18. 18.What is the 29th term of the AP 14, 16, 18, 20, …? (a) 70 (b) 72 (c) 58 (d) 56
  19. 19.What is the 15th term of the AP 11, 14, 17, 20, …? (a) 45 (b) 42 (c) 53 (d) 56
  20. 20.What is the missing term in the AP 9, ?, 17, 21, 25? (a) 12 (b) 13 (c) 14 (d) 17
  21. 21.What is the sum of the first 7 terms of the AP 10, 14, 18, …? (a) 308 (b) 154 (c) 34 (d) 168
  22. 22.What is the sum of the first 11 terms of the AP 3, 9, 15, …? (a) 63 (b) 396 (c) 363 (d) 726
  23. 23.What is the sum of all the whole numbers from 1 to 18? (a) 171 (b) 342 (c) 153 (d) 162
  24. 24.What is the 34th term of the AP 16, 21, 26, 31, …? (a) 186 (b) 181 (c) 170 (d) 165
  25. 25.What is the sum of the first 6 terms of the AP 9, 12, 15, …? (a) 24 (b) 198 (c) 99 (d) 108
  26. 26.What is the sum of the first 6 terms of the AP 7, 8, 9, …? (a) 60 (b) 114 (c) 12 (d) 57
  27. 27.What is the missing term in the AP 15, 24, ?, 42, 51? (a) 34 (b) 32 (c) 42 (d) 33
  28. 28.What is the sum of all the whole numbers from 1 to 63? (a) 4032 (b) 2017 (c) 2016 (d) 1953
  29. 29.What is the missing term in the AP 18, 21, ?, 27, 30? (a) 25 (b) 27 (c) 24 (d) 23
  30. 30.What is the sum of the first 11 terms of the AP 4, 9, 14, …? (a) 638 (b) 324 (c) 54 (d) 319
  31. 31.What is the sum of all the whole numbers from 1 to 50? (a) 1225 (b) 2550 (c) 1250 (d) 1275
  32. 32.What is the sum of the first 16 odd numbers (1 + 3 + 5 + …)? (a) 256 (b) 136 (c) 272 (d) 31
  33. 33.What is the sum of the first 10 terms of the AP 2, 3, 4, …? (a) 65 (b) 11 (c) 70 (d) 130
  34. 34.What is the 10th term of the AP 3, 10, 17, 24, …? (a) 66 (b) 70 (c) 63 (d) 73
  35. 35.What is the missing term in the AP 5, 13, 21, ?, 37? (a) 28 (b) 30 (c) 29 (d) 37
  36. 36.What is the 40th term of the AP 13, 21, 29, 37, …? (a) 312 (b) 320 (c) 325 (d) 333
  37. 37.What is the 18th term of the AP 13, 18, 23, 28, …? (a) 90 (b) 98 (c) 85 (d) 103
  38. 38.What is the 18th term of the AP 11, 14, 17, 20, …? (a) 51 (b) 65 (c) 54 (d) 62
  39. 39.What is the 23rd term of the AP 6, 11, 16, 21, …? (a) 115 (b) 121 (c) 116 (d) 110
  40. 40.What is the 18th term of the AP 3, 11, 19, 27, …? (a) 144 (b) 139 (c) 136 (d) 147

Answer key

  1. 189
  2. 39th
  3. 181
  4. 210
  5. 3321
  6. 63
  7. 120
  8. 29
  9. 2211
  10. 91
  11. 33
  12. 265
  13. 231
  14. 107
  15. 20
  16. 101
  17. 12
  18. 70
  19. 53
  20. 13
  21. 154
  22. 363
  23. 171
  24. 181
  25. 99
  26. 57
  27. 33
  28. 2016
  29. 24
  30. 319
  31. 1275
  32. 256
  33. 65
  34. 66
  35. 29
  36. 325
  37. 98
  38. 62
  39. 116
  40. 139

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