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Arithmetic Progression Worksheet for Olympiad

Maths Olympiad topic 29: Sequences and AP · Set 538 · 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 20th term of the AP 1, 5, 9, 13, …? (a) 81 (b) 76 (c) 80 (d) 77
  2. 2.What is the 15th term of the AP 11, 17, 23, 29, …? (a) 90 (b) 84 (c) 101 (d) 95
  3. 3.What is the 19th term of the AP 1, 9, 17, 25, …? (a) 145 (b) 153 (c) 152 (d) 144
  4. 4.What is the sum of all the whole numbers from 1 to 64? (a) 2048 (b) 2080 (c) 4160 (d) 2016
  5. 5.What is the 30th term of the AP 3, 8, 13, 18, …? (a) 153 (b) 145 (c) 150 (d) 148
  6. 6.What is the 32nd term of the AP 10, 13, 16, 19, …? (a) 106 (b) 93 (c) 103 (d) 96
  7. 7.What is the 14th term of the AP 19, 21, 23, 25, …? (a) 28 (b) 47 (c) 45 (d) 26
  8. 8.What is the missing term in the AP 14, 17, 20, ?, 26? (a) 26 (b) 23 (c) 24 (d) 22
  9. 9.What is the sum of all the whole numbers from 1 to 48? (a) 2352 (b) 1128 (c) 1152 (d) 1176
  10. 10.What is the sum of the first 7 odd numbers (1 + 3 + 5 + …)? (a) 56 (b) 49 (c) 13 (d) 28
  11. 11.What is the 36th term of the AP 16, 21, 26, 31, …? (a) 191 (b) 196 (c) 175 (d) 180
  12. 12.What is the 25th term of the AP 16, 22, 28, 34, …? (a) 150 (b) 144 (c) 160 (d) 166
  13. 13.What is the missing term in the AP 2, 5, 8, ?, 14? (a) 10 (b) 12 (c) 14 (d) 11
  14. 14.What is the sum of all the whole numbers from 1 to 82? (a) 3321 (b) 6806 (c) 3362 (d) 3403
  15. 15.What is the missing term in the AP 4, ?, 12, 16, 20? (a) 7 (b) 9 (c) 12 (d) 8
  16. 16.What is the sum of the first 18 odd numbers (1 + 3 + 5 + …)? (a) 171 (b) 35 (c) 324 (d) 342
  17. 17.What is the sum of the first 24 odd numbers (1 + 3 + 5 + …)? (a) 600 (b) 300 (c) 47 (d) 576
  18. 18.What is the 16th term of the AP 7, 14, 21, 28, …? (a) 119 (b) 105 (c) 113 (d) 112
  19. 19.What is the 37th term of the AP 13, 15, 17, 19, …? (a) 87 (b) 72 (c) 85 (d) 74
  20. 20.What is the 21st term of the AP 13, 21, 29, 37, …? (a) 168 (b) 181 (c) 173 (d) 160
  21. 21.What is the 38th term of the AP 5, 12, 19, 26, …? (a) 259 (b) 266 (c) 264 (d) 271
  22. 22.Which term of the AP 15, 20, 25, 30, … is 105? (a) 21st (b) 18th (c) 20th (d) 19th
  23. 23.What is the 17th term of the AP 10, 14, 18, 22, …? (a) 74 (b) 68 (c) 64 (d) 78
  24. 24.What is the 32nd term of the AP 3, 12, 21, 30, …? (a) 282 (b) 288 (c) 279 (d) 291
  25. 25.What is the 13th term of the AP 16, 19, 22, 25, …? (a) 55 (b) 36 (c) 52 (d) 39
  26. 26.What is the 32nd term of the AP 17, 21, 25, 29, …? (a) 124 (b) 141 (c) 128 (d) 145
  27. 27.What is the 12th term of the AP 8, 13, 18, 23, …? (a) 55 (b) 60 (c) 63 (d) 68
  28. 28.What is the 38th term of the AP 17, 23, 29, 35, …? (a) 239 (b) 228 (c) 245 (d) 222
  29. 29.What is the 17th term of the AP 11, 15, 19, 23, …? (a) 64 (b) 79 (c) 75 (d) 68
  30. 30.What is the 39th term of the AP 5, 9, 13, 17, …? (a) 157 (b) 156 (c) 152 (d) 161
  31. 31.What is the 33rd term of the AP 7, 16, 25, 34, …? (a) 295 (b) 297 (c) 304 (d) 288
  32. 32.What is the 28th term of the AP 5, 13, 21, 29, …? (a) 224 (b) 229 (c) 221 (d) 216
  33. 33.What is the missing term in the AP 11, ?, 29, 38, 47? (a) 29 (b) 21 (c) 19 (d) 20
  34. 34.What is the sum of the first 5 terms of the AP 6, 11, 16, …? (a) 80 (b) 85 (c) 26 (d) 160
  35. 35.What is the sum of the first 6 terms of the AP 10, 13, 16, …? (a) 25 (b) 114 (c) 105 (d) 210
  36. 36.What is the 13th term of the AP 6, 11, 16, 21, …? (a) 66 (b) 65 (c) 71 (d) 60
  37. 37.What is the missing term in the AP 17, 21, 25, ?, 33? (a) 29 (b) 28 (c) 33 (d) 30
  38. 38.What is the sum of the first 19 odd numbers (1 + 3 + 5 + …)? (a) 380 (b) 361 (c) 190 (d) 37
  39. 39.What is the sum of the first 5 terms of the AP 7, 13, 19, …? (a) 110 (b) 190 (c) 95 (d) 31
  40. 40.What is the 26th term of the AP 12, 21, 30, 39, …? (a) 234 (b) 237 (c) 225 (d) 246

Answer key

  1. 77
  2. 95
  3. 145
  4. 2080
  5. 148
  6. 103
  7. 45
  8. 23
  9. 1176
  10. 49
  11. 191
  12. 160
  13. 11
  14. 3403
  15. 8
  16. 324
  17. 576
  18. 112
  19. 85
  20. 173
  21. 264
  22. 19th
  23. 74
  24. 282
  25. 52
  26. 141
  27. 63
  28. 239
  29. 75
  30. 157
  31. 295
  32. 221
  33. 20
  34. 80
  35. 105
  36. 66
  37. 29
  38. 361
  39. 95
  40. 237

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