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Arithmetic Progression Worksheet for Olympiad

Maths Olympiad topic 29: Sequences and AP · Set 233 · 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 28th term of the AP 20, 28, 36, 44, …? (a) 236 (b) 216 (c) 224 (d) 244
  2. 2.What is the sum of all the whole numbers from 1 to 36? (a) 1332 (b) 630 (c) 666 (d) 648
  3. 3.What is the sum of the first 6 terms of the AP 4, 8, 12, …? (a) 168 (b) 24 (c) 84 (d) 96
  4. 4.What is the sum of all the whole numbers from 1 to 63? (a) 4032 (b) 2016 (c) 2017 (d) 1953
  5. 5.What is the sum of the first 5 terms of the AP 1, 2, 3, …? (a) 30 (b) 5 (c) 15 (d) 16
  6. 6.What is the missing term in the AP 9, ?, 21, 27, 33? (a) 16 (b) 15 (c) 14 (d) 21
  7. 7.What is the sum of the first 6 terms of the AP 1, 3, 5, …? (a) 36 (b) 11 (c) 42 (d) 72
  8. 8.What is the sum of the first 6 terms of the AP 2, 6, 10, …? (a) 72 (b) 144 (c) 22 (d) 84
  9. 9.What is the sum of all the whole numbers from 1 to 62? (a) 1953 (b) 1891 (c) 1922 (d) 3906
  10. 10.What is the 19th term of the AP 5, 9, 13, 17, …? (a) 81 (b) 76 (c) 72 (d) 77
  11. 11.What is the sum of the first 11 terms of the AP 5, 9, 13, …? (a) 275 (b) 550 (c) 45 (d) 297
  12. 12.What is the sum of the first 20 odd numbers (1 + 3 + 5 + …)? (a) 210 (b) 39 (c) 400 (d) 420
  13. 13.What is the 11th term of the AP 17, 24, 31, 38, …? (a) 94 (b) 87 (c) 70 (d) 77
  14. 14.What is the 22nd term of the AP 7, 16, 25, 34, …? (a) 196 (b) 189 (c) 205 (d) 198
  15. 15.What is the 17th term of the AP 5, 13, 21, 29, …? (a) 141 (b) 136 (c) 128 (d) 133
  16. 16.What is the 22nd term of the AP 4, 6, 8, 10, …? (a) 42 (b) 46 (c) 44 (d) 48
  17. 17.What is the sum of the first 15 odd numbers (1 + 3 + 5 + …)? (a) 120 (b) 29 (c) 240 (d) 225
  18. 18.What is the 23rd term of the AP 9, 11, 13, 15, …? (a) 53 (b) 55 (c) 44 (d) 46
  19. 19.What is the 29th term of the AP 9, 14, 19, 24, …? (a) 154 (b) 149 (c) 145 (d) 140
  20. 20.What is the sum of all the whole numbers from 1 to 90? (a) 4050 (b) 8190 (c) 4005 (d) 4095
  21. 21.What is the missing term in the AP 11, 20, ?, 38, 47? (a) 30 (b) 29 (c) 28 (d) 38
  22. 22.What is the sum of the first 30 odd numbers (1 + 3 + 5 + …)? (a) 465 (b) 900 (c) 930 (d) 59
  23. 23.What is the sum of the first 23 odd numbers (1 + 3 + 5 + …)? (a) 45 (b) 552 (c) 276 (d) 529
  24. 24.What is the 31st term of the AP 19, 21, 23, 25, …? (a) 60 (b) 79 (c) 81 (d) 62
  25. 25.What is the sum of all the whole numbers from 1 to 39? (a) 741 (b) 1560 (c) 781 (d) 780
  26. 26.What is the 24th term of the AP 11, 19, 27, 35, …? (a) 195 (b) 203 (c) 184 (d) 192
  27. 27.What is the sum of the first 11 terms of the AP 8, 11, 14, …? (a) 506 (b) 256 (c) 38 (d) 253
  28. 28.Which term of the AP 18, 27, 36, 45, … is 135? (a) 15th (b) 16th (c) 13th (d) 14th
  29. 29.What is the sum of the first 6 terms of the AP 6, 8, 10, …? (a) 16 (b) 132 (c) 72 (d) 66
  30. 30.What is the sum of the first 10 odd numbers (1 + 3 + 5 + …)? (a) 100 (b) 19 (c) 110 (d) 55
  31. 31.What is the sum of the first 8 terms of the AP 4, 9, 14, …? (a) 39 (b) 344 (c) 172 (d) 192
  32. 32.What is the 10th term of the AP 19, 28, 37, 46, …? (a) 90 (b) 81 (c) 100 (d) 109
  33. 33.What is the 25th term of the AP 9, 17, 25, 33, …? (a) 200 (b) 192 (c) 201 (d) 209
  34. 34.What is the sum of all the whole numbers from 1 to 27? (a) 351 (b) 379 (c) 756 (d) 378
  35. 35.What is the 33rd term of the AP 3, 7, 11, 15, …? (a) 132 (b) 131 (c) 128 (d) 135
  36. 36.What is the sum of the first 5 terms of the AP 2, 3, 4, …? (a) 21 (b) 40 (c) 6 (d) 20
  37. 37.Which term of the AP 13, 21, 29, 37, … is 285? (a) 36th (b) 34th (c) 37th (d) 35th
  38. 38.What is the missing term in the AP 5, 10, 15, ?, 25? (a) 25 (b) 20 (c) 21 (d) 19
  39. 39.What is the 24th term of the AP 6, 11, 16, 21, …? (a) 115 (b) 126 (c) 120 (d) 121
  40. 40.What is the 30th term of the AP 20, 25, 30, 35, …? (a) 145 (b) 165 (c) 150 (d) 170

Answer key

  1. 236
  2. 666
  3. 84
  4. 2016
  5. 15
  6. 15
  7. 36
  8. 72
  9. 1953
  10. 77
  11. 275
  12. 400
  13. 87
  14. 196
  15. 133
  16. 46
  17. 225
  18. 53
  19. 149
  20. 4095
  21. 29
  22. 900
  23. 529
  24. 79
  25. 780
  26. 195
  27. 253
  28. 14th
  29. 66
  30. 100
  31. 172
  32. 100
  33. 201
  34. 378
  35. 131
  36. 20
  37. 35th
  38. 20
  39. 121
  40. 165

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