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Arithmetic Progression Worksheet for Olympiad

Maths Olympiad topic 29: Sequences and AP · Set 989 · 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 38th term of the AP 7, 10, 13, 16, …? (a) 121 (b) 111 (c) 118 (d) 114
  2. 2.What is the missing term in the AP 4, 12, ?, 28, 36? (a) 28 (b) 19 (c) 21 (d) 20
  3. 3.What is the 17th term of the AP 6, 13, 20, 27, …? (a) 119 (b) 125 (c) 112 (d) 118
  4. 4.What is the sum of the first 14 odd numbers (1 + 3 + 5 + …)? (a) 105 (b) 27 (c) 196 (d) 210
  5. 5.What is the sum of the first 19 odd numbers (1 + 3 + 5 + …)? (a) 37 (b) 190 (c) 361 (d) 380
  6. 6.What is the sum of the first 12 terms of the AP 8, 13, 18, …? (a) 456 (b) 63 (c) 426 (d) 852
  7. 7.What is the missing term in the AP 3, 12, ?, 30, 39? (a) 30 (b) 20 (c) 21 (d) 22
  8. 8.What is the sum of the first 5 odd numbers (1 + 3 + 5 + …)? (a) 9 (b) 25 (c) 30 (d) 15
  9. 9.Which term of the AP 13, 16, 19, 22, … is 106? (a) 32nd (b) 33rd (c) 31st (d) 34th
  10. 10.What is the 27th term of the AP 6, 13, 20, 27, …? (a) 195 (b) 182 (c) 189 (d) 188
  11. 11.What is the sum of the first 12 terms of the AP 7, 10, 13, …? (a) 300 (b) 564 (c) 282 (d) 40
  12. 12.What is the 22nd term of the AP 10, 17, 24, 31, …? (a) 164 (b) 147 (c) 154 (d) 157
  13. 13.What is the 31st term of the AP 17, 24, 31, 38, …? (a) 227 (b) 217 (c) 210 (d) 234
  14. 14.What is the 34th term of the AP 18, 27, 36, 45, …? (a) 297 (b) 306 (c) 324 (d) 315
  15. 15.What is the sum of the first 8 terms of the AP 5, 11, 17, …? (a) 232 (b) 47 (c) 416 (d) 208
  16. 16.What is the 17th term of the AP 20, 27, 34, 41, …? (a) 112 (b) 132 (c) 119 (d) 139
  17. 17.What is the sum of the first 12 terms of the AP 9, 10, 11, …? (a) 180 (b) 20 (c) 348 (d) 174
  18. 18.What is the sum of all the whole numbers from 1 to 74? (a) 2738 (b) 2775 (c) 5550 (d) 2701
  19. 19.What is the sum of all the whole numbers from 1 to 15? (a) 240 (b) 120 (c) 105 (d) 121
  20. 20.What is the sum of the first 6 terms of the AP 7, 8, 9, …? (a) 60 (b) 57 (c) 12 (d) 114
  21. 21.What is the 37th term of the AP 19, 23, 27, 31, …? (a) 148 (b) 167 (c) 144 (d) 163
  22. 22.What is the sum of all the whole numbers from 1 to 20? (a) 420 (b) 190 (c) 210 (d) 200
  23. 23.What is the 29th term of the AP 18, 27, 36, 45, …? (a) 270 (b) 252 (c) 261 (d) 279
  24. 24.What is the 30th term of the AP 2, 4, 6, 8, …? (a) 58 (b) 60 (c) 61 (d) 62
  25. 25.What is the sum of the first 6 terms of the AP 7, 13, 19, …? (a) 264 (b) 132 (c) 37 (d) 150
  26. 26.What is the sum of the first 7 terms of the AP 1, 6, 11, …? (a) 112 (b) 224 (c) 117 (d) 31
  27. 27.What is the sum of the first 5 terms of the AP 3, 6, 9, …? (a) 48 (b) 90 (c) 45 (d) 15
  28. 28.What is the sum of all the whole numbers from 1 to 35? (a) 631 (b) 1260 (c) 595 (d) 630
  29. 29.What is the 13th term of the AP 6, 15, 24, 33, …? (a) 114 (b) 117 (c) 123 (d) 108
  30. 30.What is the missing term in the AP 6, ?, 14, 18, 22? (a) 11 (b) 14 (c) 10 (d) 9
  31. 31.What is the sum of all the whole numbers from 1 to 26? (a) 325 (b) 351 (c) 702 (d) 338
  32. 32.What is the 10th term of the AP 17, 21, 25, 29, …? (a) 53 (b) 57 (c) 40 (d) 36
  33. 33.What is the sum of the first 10 terms of the AP 7, 13, 19, …? (a) 680 (b) 370 (c) 61 (d) 340
  34. 34.What is the sum of the first 10 terms of the AP 4, 8, 12, …? (a) 40 (b) 240 (c) 440 (d) 220
  35. 35.What is the missing term in the AP 14, 23, ?, 41, 50? (a) 32 (b) 31 (c) 33 (d) 41
  36. 36.What is the sum of the first 12 terms of the AP 4, 5, 6, …? (a) 15 (b) 120 (c) 228 (d) 114
  37. 37.What is the sum of the first 9 terms of the AP 1, 2, 3, …? (a) 90 (b) 45 (c) 46 (d) 9
  38. 38.What is the sum of all the whole numbers from 1 to 70? (a) 2485 (b) 4970 (c) 2415 (d) 2450
  39. 39.Which term of the AP 13, 19, 25, 31, … is 187? (a) 31st (b) 30th (c) 32nd (d) 29th
  40. 40.What is the sum of all the whole numbers from 1 to 22? (a) 506 (b) 253 (c) 242 (d) 231

Answer key

  1. 118
  2. 20
  3. 118
  4. 196
  5. 361
  6. 426
  7. 21
  8. 25
  9. 32nd
  10. 188
  11. 282
  12. 157
  13. 227
  14. 315
  15. 208
  16. 132
  17. 174
  18. 2775
  19. 120
  20. 57
  21. 163
  22. 210
  23. 270
  24. 60
  25. 132
  26. 112
  27. 45
  28. 630
  29. 114
  30. 10
  31. 351
  32. 53
  33. 340
  34. 220
  35. 32
  36. 114
  37. 45
  38. 2485
  39. 30th
  40. 253

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