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Arithmetic Progression Worksheet for Olympiad

Maths Olympiad topic 29: Sequences and AP · Set 396 · 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 34th term of the AP 20, 22, 24, 26, …? (a) 86 (b) 66 (c) 68 (d) 88
  2. 2.What is the sum of all the whole numbers from 1 to 86? (a) 7482 (b) 3698 (c) 3741 (d) 3655
  3. 3.What is the sum of the first 6 terms of the AP 7, 9, 11, …? (a) 78 (b) 17 (c) 72 (d) 144
  4. 4.What is the sum of the first 12 odd numbers (1 + 3 + 5 + …)? (a) 144 (b) 78 (c) 156 (d) 23
  5. 5.What is the sum of the first 9 terms of the AP 3, 7, 11, …? (a) 35 (b) 342 (c) 189 (d) 171
  6. 6.What is the missing term in the AP 18, 24, 30, ?, 42? (a) 37 (b) 35 (c) 36 (d) 42
  7. 7.What is the sum of the first 11 terms of the AP 6, 9, 12, …? (a) 36 (b) 231 (c) 462 (d) 234
  8. 8.What is the sum of the first 9 terms of the AP 1, 2, 3, …? (a) 46 (b) 90 (c) 9 (d) 45
  9. 9.Which term of the AP 8, 13, 18, 23, … is 108? (a) 23rd (b) 20th (c) 22nd (d) 21st
  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.Which term of the AP 2, 10, 18, 26, … is 130? (a) 16th (b) 17th (c) 18th (d) 19th
  12. 12.What is the missing term in the AP 4, ?, 16, 22, 28? (a) 11 (b) 16 (c) 10 (d) 9
  13. 13.What is the sum of the first 9 terms of the AP 1, 5, 9, …? (a) 306 (b) 33 (c) 171 (d) 153
  14. 14.What is the sum of the first 10 odd numbers (1 + 3 + 5 + …)? (a) 19 (b) 55 (c) 110 (d) 100
  15. 15.What is the missing term in the AP 1, 5, ?, 13, 17? (a) 9 (b) 8 (c) 10 (d) 13
  16. 16.What is the sum of all the whole numbers from 1 to 88? (a) 3828 (b) 3872 (c) 3916 (d) 7832
  17. 17.What is the sum of the first 11 odd numbers (1 + 3 + 5 + …)? (a) 66 (b) 21 (c) 121 (d) 132
  18. 18.What is the 34th term of the AP 18, 24, 30, 36, …? (a) 216 (b) 222 (c) 204 (d) 198
  19. 19.What is the 40th term of the AP 8, 11, 14, 17, …? (a) 128 (b) 120 (c) 125 (d) 117
  20. 20.What is the sum of the first 24 odd numbers (1 + 3 + 5 + …)? (a) 47 (b) 300 (c) 600 (d) 576
  21. 21.What is the 23rd term of the AP 6, 9, 12, 15, …? (a) 75 (b) 66 (c) 72 (d) 69
  22. 22.What is the sum of all the whole numbers from 1 to 65? (a) 2145 (b) 2080 (c) 4290 (d) 2146
  23. 23.What is the sum of the first 10 terms of the AP 6, 8, 10, …? (a) 300 (b) 160 (c) 24 (d) 150
  24. 24.What is the 16th term of the AP 20, 28, 36, 44, …? (a) 128 (b) 120 (c) 140 (d) 148
  25. 25.What is the missing term in the AP 13, 18, 23, ?, 33? (a) 33 (b) 28 (c) 29 (d) 27
  26. 26.What is the 23rd term of the AP 7, 15, 23, 31, …? (a) 191 (b) 184 (c) 176 (d) 183
  27. 27.What is the 23rd term of the AP 20, 22, 24, 26, …? (a) 66 (b) 46 (c) 64 (d) 44
  28. 28.What is the sum of all the whole numbers from 1 to 27? (a) 379 (b) 756 (c) 351 (d) 378
  29. 29.What is the sum of the first 10 terms of the AP 3, 8, 13, …? (a) 280 (b) 510 (c) 255 (d) 48
  30. 30.Which term of the AP 3, 6, 9, 12, … is 108? (a) 37th (b) 36th (c) 35th (d) 38th
  31. 31.Which term of the AP 1, 10, 19, 28, … is 325? (a) 39th (b) 37th (c) 36th (d) 38th
  32. 32.What is the missing term in the AP 17, ?, 21, 23, 25? (a) 18 (b) 19 (c) 21 (d) 20
  33. 33.What is the missing term in the AP 10, 13, ?, 19, 22? (a) 16 (b) 19 (c) 15 (d) 17
  34. 34.Which term of the AP 1, 6, 11, 16, … is 81? (a) 17th (b) 19th (c) 18th (d) 16th
  35. 35.What is the sum of the first 19 odd numbers (1 + 3 + 5 + …)? (a) 190 (b) 37 (c) 361 (d) 380
  36. 36.What is the sum of the first 8 terms of the AP 8, 9, 10, …? (a) 184 (b) 15 (c) 92 (d) 96
  37. 37.What is the 24th term of the AP 3, 7, 11, 15, …? (a) 99 (b) 96 (c) 95 (d) 92
  38. 38.What is the sum of the first 7 terms of the AP 2, 7, 12, …? (a) 32 (b) 238 (c) 119 (d) 124
  39. 39.Which term of the AP 3, 9, 15, 21, … is 87? (a) 17th (b) 16th (c) 15th (d) 14th
  40. 40.What is the sum of all the whole numbers from 1 to 63? (a) 1953 (b) 2017 (c) 2016 (d) 4032

Answer key

  1. 86
  2. 3741
  3. 72
  4. 144
  5. 171
  6. 36
  7. 231
  8. 45
  9. 21st
  10. 441
  11. 17th
  12. 10
  13. 153
  14. 100
  15. 9
  16. 3916
  17. 121
  18. 216
  19. 125
  20. 576
  21. 72
  22. 2145
  23. 150
  24. 140
  25. 28
  26. 183
  27. 64
  28. 378
  29. 255
  30. 36th
  31. 37th
  32. 19
  33. 16
  34. 17th
  35. 361
  36. 92
  37. 95
  38. 119
  39. 15th
  40. 2016

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