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Arithmetic Progression Worksheet for Olympiad

Maths Olympiad topic 29: Sequences and AP · Set 858 · 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 40th term of the AP 17, 22, 27, 32, …? (a) 212 (b) 200 (c) 195 (d) 217
  2. 2.What is the sum of all the whole numbers from 1 to 82? (a) 3362 (b) 3321 (c) 3403 (d) 6806
  3. 3.What is the 14th term of the AP 2, 6, 10, 14, …? (a) 56 (b) 58 (c) 52 (d) 54
  4. 4.What is the 11th term of the AP 11, 13, 15, 17, …? (a) 31 (b) 33 (c) 22 (d) 20
  5. 5.What is the 14th term of the AP 8, 14, 20, 26, …? (a) 86 (b) 84 (c) 92 (d) 78
  6. 6.What is the sum of the first 13 odd numbers (1 + 3 + 5 + …)? (a) 169 (b) 91 (c) 182 (d) 25
  7. 7.What is the 22nd term of the AP 4, 10, 16, 22, …? (a) 130 (b) 136 (c) 132 (d) 126
  8. 8.What is the sum of the first 22 odd numbers (1 + 3 + 5 + …)? (a) 253 (b) 484 (c) 43 (d) 506
  9. 9.What is the 25th term of the AP 13, 16, 19, 22, …? (a) 75 (b) 72 (c) 85 (d) 88
  10. 10.What is the sum of the first 21 odd numbers (1 + 3 + 5 + …)? (a) 462 (b) 41 (c) 441 (d) 231
  11. 11.What is the 27th term of the AP 3, 5, 7, 9, …? (a) 57 (b) 52 (c) 54 (d) 55
  12. 12.Which term of the AP 6, 10, 14, 18, … is 154? (a) 40th (b) 37th (c) 39th (d) 38th
  13. 13.What is the sum of all the whole numbers from 1 to 77? (a) 3003 (b) 2926 (c) 6006 (d) 3004
  14. 14.What is the missing term in the AP 13, 17, 21, ?, 29? (a) 24 (b) 29 (c) 25 (d) 26
  15. 15.What is the 35th term of the AP 19, 26, 33, 40, …? (a) 264 (b) 238 (c) 257 (d) 245
  16. 16.What is the 21st term of the AP 10, 13, 16, 19, …? (a) 60 (b) 63 (c) 70 (d) 73
  17. 17.What is the sum of the first 9 terms of the AP 9, 14, 19, …? (a) 266 (b) 261 (c) 522 (d) 49
  18. 18.Which term of the AP 9, 13, 17, 21, … is 153? (a) 37th (b) 38th (c) 36th (d) 39th
  19. 19.What is the sum of the first 12 odd numbers (1 + 3 + 5 + …)? (a) 23 (b) 78 (c) 156 (d) 144
  20. 20.What is the sum of all the whole numbers from 1 to 100? (a) 5050 (b) 4950 (c) 5000 (d) 10100
  21. 21.What is the 39th term of the AP 7, 10, 13, 16, …? (a) 124 (b) 121 (c) 114 (d) 117
  22. 22.What is the sum of all the whole numbers from 1 to 34? (a) 595 (b) 1190 (c) 578 (d) 561
  23. 23.What is the 32nd term of the AP 19, 28, 37, 46, …? (a) 288 (b) 279 (c) 307 (d) 298
  24. 24.What is the 39th term of the AP 8, 10, 12, 14, …? (a) 84 (b) 78 (c) 86 (d) 76
  25. 25.Which term of the AP 1, 6, 11, 16, … is 161? (a) 35th (b) 33rd (c) 34th (d) 32nd
  26. 26.What is the sum of all the whole numbers from 1 to 59? (a) 1711 (b) 1770 (c) 3540 (d) 1771
  27. 27.What is the missing term in the AP 8, ?, 24, 32, 40? (a) 17 (b) 24 (c) 15 (d) 16
  28. 28.What is the 11th term of the AP 15, 24, 33, 42, …? (a) 114 (b) 90 (c) 99 (d) 105
  29. 29.What is the sum of the first 27 odd numbers (1 + 3 + 5 + …)? (a) 729 (b) 756 (c) 53 (d) 378
  30. 30.What is the 20th term of the AP 12, 16, 20, 24, …? (a) 80 (b) 92 (c) 76 (d) 88
  31. 31.What is the sum of all the whole numbers from 1 to 19? (a) 190 (b) 171 (c) 191 (d) 380
  32. 32.What is the 28th term of the AP 17, 19, 21, 23, …? (a) 56 (b) 54 (c) 73 (d) 71
  33. 33.What is the sum of the first 20 odd numbers (1 + 3 + 5 + …)? (a) 400 (b) 420 (c) 210 (d) 39
  34. 34.What is the sum of the first 10 terms of the AP 3, 9, 15, …? (a) 300 (b) 57 (c) 330 (d) 600
  35. 35.What is the sum of the first 8 terms of the AP 10, 15, 20, …? (a) 45 (b) 240 (c) 220 (d) 440
  36. 36.What is the 23rd term of the AP 2, 9, 16, 23, …? (a) 161 (b) 154 (c) 156 (d) 163
  37. 37.What is the 12th term of the AP 6, 15, 24, 33, …? (a) 114 (b) 108 (c) 105 (d) 99
  38. 38.What is the 25th term of the AP 7, 9, 11, 13, …? (a) 57 (b) 55 (c) 50 (d) 48
  39. 39.Which term of the AP 8, 14, 20, 26, … is 50? (a) 7th (b) 10th (c) 9th (d) 8th
  40. 40.What is the sum of the first 28 odd numbers (1 + 3 + 5 + …)? (a) 55 (b) 812 (c) 784 (d) 406

Answer key

  1. 212
  2. 3403
  3. 54
  4. 31
  5. 86
  6. 169
  7. 130
  8. 484
  9. 85
  10. 441
  11. 55
  12. 38th
  13. 3003
  14. 25
  15. 257
  16. 70
  17. 261
  18. 37th
  19. 144
  20. 5050
  21. 121
  22. 595
  23. 298
  24. 84
  25. 33rd
  26. 1770
  27. 16
  28. 105
  29. 729
  30. 88
  31. 190
  32. 71
  33. 400
  34. 300
  35. 220
  36. 156
  37. 105
  38. 55
  39. 8th
  40. 784

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