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Arithmetic Progression Worksheet for Olympiad

Maths Olympiad topic 29: Sequences and AP · Set 620 · 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 all the whole numbers from 1 to 63? (a) 2016 (b) 4032 (c) 1953 (d) 2017
  2. 2.What is the missing term in the AP 19, ?, 35, 43, 51? (a) 26 (b) 35 (c) 27 (d) 28
  3. 3.What is the sum of all the whole numbers from 1 to 30? (a) 450 (b) 930 (c) 465 (d) 435
  4. 4.Which term of the AP 16, 18, 20, 22, … is 82? (a) 33rd (b) 35th (c) 41st (d) 34th
  5. 5.What is the sum of the first 11 odd numbers (1 + 3 + 5 + …)? (a) 66 (b) 121 (c) 132 (d) 21
  6. 6.What is the 17th term of the AP 18, 25, 32, 39, …? (a) 119 (b) 112 (c) 137 (d) 130
  7. 7.What is the 32nd term of the AP 4, 9, 14, 19, …? (a) 159 (b) 160 (c) 164 (d) 155
  8. 8.Which term of the AP 7, 13, 19, 25, … is 211? (a) 36th (b) 34th (c) 37th (d) 35th
  9. 9.What is the sum of the first 9 terms of the AP 8, 11, 14, …? (a) 360 (b) 32 (c) 183 (d) 180
  10. 10.What is the sum of the first 15 odd numbers (1 + 3 + 5 + …)? (a) 240 (b) 225 (c) 29 (d) 120
  11. 11.What is the 35th term of the AP 13, 15, 17, 19, …? (a) 70 (b) 68 (c) 83 (d) 81
  12. 12.What is the 36th term of the AP 3, 12, 21, 30, …? (a) 315 (b) 324 (c) 318 (d) 327
  13. 13.What is the sum of all the whole numbers from 1 to 33? (a) 562 (b) 528 (c) 1122 (d) 561
  14. 14.What is the sum of the first 9 terms of the AP 6, 7, 8, …? (a) 91 (b) 90 (c) 180 (d) 14
  15. 15.What is the sum of the first 6 terms of the AP 2, 4, 6, …? (a) 12 (b) 48 (c) 84 (d) 42
  16. 16.What is the sum of the first 10 terms of the AP 2, 4, 6, …? (a) 120 (b) 20 (c) 110 (d) 220
  17. 17.What is the sum of the first 28 odd numbers (1 + 3 + 5 + …)? (a) 406 (b) 784 (c) 55 (d) 812
  18. 18.What is the sum of all the whole numbers from 1 to 100? (a) 4950 (b) 5000 (c) 5050 (d) 10100
  19. 19.Which term of the AP 13, 16, 19, 22, … is 121? (a) 39th (b) 38th (c) 37th (d) 36th
  20. 20.What is the sum of the first 5 terms of the AP 1, 4, 7, …? (a) 38 (b) 35 (c) 70 (d) 13
  21. 21.What is the sum of all the whole numbers from 1 to 95? (a) 4465 (b) 4561 (c) 4560 (d) 9120
  22. 22.What is the 16th term of the AP 20, 23, 26, 29, …? (a) 48 (b) 65 (c) 68 (d) 45
  23. 23.What is the missing term in the AP 18, ?, 32, 39, 46? (a) 25 (b) 32 (c) 26 (d) 24
  24. 24.What is the sum of the first 24 odd numbers (1 + 3 + 5 + …)? (a) 300 (b) 600 (c) 576 (d) 47
  25. 25.What is the 19th term of the AP 13, 21, 29, 37, …? (a) 144 (b) 165 (c) 157 (d) 152
  26. 26.What is the sum of the first 12 terms of the AP 10, 13, 16, …? (a) 636 (b) 43 (c) 318 (d) 336
  27. 27.What is the 10th term of the AP 7, 11, 15, 19, …? (a) 36 (b) 43 (c) 40 (d) 47
  28. 28.What is the 34th term of the AP 4, 10, 16, 22, …? (a) 208 (b) 198 (c) 204 (d) 202
  29. 29.What is the sum of the first 7 odd numbers (1 + 3 + 5 + …)? (a) 13 (b) 56 (c) 49 (d) 28
  30. 30.What is the sum of the first 5 terms of the AP 4, 5, 6, …? (a) 8 (b) 60 (c) 31 (d) 30
  31. 31.Which term of the AP 15, 17, 19, 21, … is 91? (a) 41st (b) 38th (c) 39th (d) 40th
  32. 32.What is the sum of the first 5 terms of the AP 2, 6, 10, …? (a) 18 (b) 100 (c) 50 (d) 60
  33. 33.Which term of the AP 16, 24, 32, 40, … is 256? (a) 32nd (b) 31st (c) 33rd (d) 30th
  34. 34.Which term of the AP 3, 5, 7, 9, … is 53? (a) 28th (b) 25th (c) 27th (d) 26th
  35. 35.What is the sum of the first 6 terms of the AP 9, 11, 13, …? (a) 168 (b) 19 (c) 84 (d) 90
  36. 36.What is the 38th term of the AP 17, 24, 31, 38, …? (a) 266 (b) 276 (c) 283 (d) 259
  37. 37.Which term of the AP 3, 6, 9, 12, … is 111? (a) 37th (b) 36th (c) 39th (d) 38th
  38. 38.What is the 34th term of the AP 20, 26, 32, 38, …? (a) 224 (b) 198 (c) 218 (d) 204
  39. 39.What is the sum of all the whole numbers from 1 to 68? (a) 2346 (b) 2312 (c) 4692 (d) 2278
  40. 40.What is the 11th term of the AP 3, 8, 13, 18, …? (a) 53 (b) 55 (c) 50 (d) 58

Answer key

  1. 2016
  2. 27
  3. 465
  4. 34th
  5. 121
  6. 130
  7. 159
  8. 35th
  9. 180
  10. 225
  11. 81
  12. 318
  13. 561
  14. 90
  15. 42
  16. 110
  17. 784
  18. 5050
  19. 37th
  20. 35
  21. 4560
  22. 65
  23. 25
  24. 576
  25. 157
  26. 318
  27. 43
  28. 202
  29. 49
  30. 30
  31. 39th
  32. 50
  33. 31st
  34. 26th
  35. 84
  36. 276
  37. 37th
  38. 218
  39. 2346
  40. 53

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