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Arithmetic Progression Worksheet for Olympiad

Maths Olympiad topic 29: Sequences and AP · Set 486 · 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 21? (a) 232 (b) 231 (c) 462 (d) 210
  2. 2.What is the sum of the first 8 terms of the AP 1, 7, 13, …? (a) 352 (b) 200 (c) 176 (d) 43
  3. 3.What is the 12th term of the AP 1, 7, 13, 19, …? (a) 66 (b) 67 (c) 72 (d) 73
  4. 4.What is the 19th term of the AP 8, 17, 26, 35, …? (a) 171 (b) 179 (c) 170 (d) 162
  5. 5.What is the sum of the first 24 odd numbers (1 + 3 + 5 + …)? (a) 600 (b) 576 (c) 300 (d) 47
  6. 6.What is the sum of the first 6 terms of the AP 2, 4, 6, …? (a) 84 (b) 48 (c) 12 (d) 42
  7. 7.Which term of the AP 4, 7, 10, 13, … is 115? (a) 37th (b) 39th (c) 38th (d) 40th
  8. 8.What is the 22nd term of the AP 6, 9, 12, 15, …? (a) 66 (b) 69 (c) 63 (d) 72
  9. 9.What is the sum of all the whole numbers from 1 to 39? (a) 741 (b) 1560 (c) 781 (d) 780
  10. 10.Which term of the AP 12, 19, 26, 33, … is 250? (a) 37th (b) 36th (c) 35th (d) 34th
  11. 11.What is the sum of the first 10 odd numbers (1 + 3 + 5 + …)? (a) 110 (b) 100 (c) 19 (d) 55
  12. 12.What is the 31st term of the AP 9, 12, 15, 18, …? (a) 93 (b) 90 (c) 99 (d) 102
  13. 13.What is the 28th term of the AP 2, 7, 12, 17, …? (a) 140 (b) 137 (c) 142 (d) 135
  14. 14.What is the 26th term of the AP 20, 22, 24, 26, …? (a) 50 (b) 72 (c) 70 (d) 52
  15. 15.What is the 24th term of the AP 4, 10, 16, 22, …? (a) 142 (b) 138 (c) 148 (d) 144
  16. 16.What is the sum of the first 30 odd numbers (1 + 3 + 5 + …)? (a) 930 (b) 465 (c) 59 (d) 900
  17. 17.What is the 40th term of the AP 14, 17, 20, 23, …? (a) 120 (b) 134 (c) 131 (d) 117
  18. 18.What is the 15th term of the AP 4, 13, 22, 31, …? (a) 135 (b) 126 (c) 130 (d) 139
  19. 19.What is the sum of the first 11 terms of the AP 9, 12, 15, …? (a) 267 (b) 528 (c) 39 (d) 264
  20. 20.What is the sum of the first 9 terms of the AP 1, 5, 9, …? (a) 33 (b) 171 (c) 153 (d) 306
  21. 21.What is the 23rd term of the AP 13, 17, 21, 25, …? (a) 101 (b) 105 (c) 92 (d) 88
  22. 22.What is the 15th term of the AP 3, 8, 13, 18, …? (a) 75 (b) 78 (c) 70 (d) 73
  23. 23.Which term of the AP 16, 24, 32, 40, … is 80? (a) 8th (b) 10th (c) 9th (d) 11th
  24. 24.What is the sum of the first 20 odd numbers (1 + 3 + 5 + …)? (a) 210 (b) 39 (c) 400 (d) 420
  25. 25.What is the 29th term of the AP 20, 29, 38, 47, …? (a) 261 (b) 272 (c) 252 (d) 281
  26. 26.What is the missing term in the AP 11, 15, ?, 23, 27? (a) 23 (b) 19 (c) 18 (d) 20
  27. 27.Which term of the AP 9, 13, 17, 21, … is 69? (a) 18th (b) 16th (c) 15th (d) 17th
  28. 28.What is the sum of the first 6 terms of the AP 2, 8, 14, …? (a) 102 (b) 204 (c) 32 (d) 120
  29. 29.What is the 20th term of the AP 6, 14, 22, 30, …? (a) 166 (b) 160 (c) 158 (d) 152
  30. 30.What is the 15th term of the AP 2, 7, 12, 17, …? (a) 70 (b) 77 (c) 75 (d) 72
  31. 31.What is the sum of the first 11 odd numbers (1 + 3 + 5 + …)? (a) 66 (b) 21 (c) 132 (d) 121
  32. 32.What is the 37th term of the AP 13, 17, 21, 25, …? (a) 157 (b) 161 (c) 148 (d) 144
  33. 33.What is the missing term in the AP 11, 18, 25, ?, 39? (a) 39 (b) 32 (c) 31 (d) 33
  34. 34.What is the sum of the first 11 terms of the AP 3, 5, 7, …? (a) 23 (b) 143 (c) 154 (d) 286
  35. 35.Which term of the AP 12, 14, 16, 18, … is 60? (a) 24th (b) 26th (c) 30th (d) 25th
  36. 36.What is the sum of the first 9 terms of the AP 2, 7, 12, …? (a) 198 (b) 203 (c) 396 (d) 42
  37. 37.What is the sum of the first 27 odd numbers (1 + 3 + 5 + …)? (a) 53 (b) 729 (c) 756 (d) 378
  38. 38.What is the 24th term of the AP 3, 12, 21, 30, …? (a) 207 (b) 210 (c) 216 (d) 219
  39. 39.What is the missing term in the AP 16, 24, ?, 40, 48? (a) 40 (b) 31 (c) 32 (d) 33
  40. 40.What is the missing term in the AP 15, ?, 31, 39, 47? (a) 31 (b) 23 (c) 24 (d) 22

Answer key

  1. 231
  2. 176
  3. 67
  4. 170
  5. 576
  6. 42
  7. 38th
  8. 69
  9. 780
  10. 35th
  11. 100
  12. 99
  13. 137
  14. 70
  15. 142
  16. 900
  17. 131
  18. 130
  19. 264
  20. 153
  21. 101
  22. 73
  23. 9th
  24. 400
  25. 272
  26. 19
  27. 16th
  28. 102
  29. 158
  30. 72
  31. 121
  32. 157
  33. 32
  34. 143
  35. 25th
  36. 198
  37. 729
  38. 210
  39. 32
  40. 23

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