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Arithmetic Progression Worksheet for Olympiad

Maths Olympiad topic 29: Sequences and AP · Set 693 · 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.Which term of the AP 16, 24, 32, 40, … is 72? (a) 7th (b) 9th (c) 10th (d) 8th
  2. 2.What is the sum of the first 8 terms of the AP 8, 10, 12, …? (a) 128 (b) 120 (c) 240 (d) 22
  3. 3.What is the sum of the first 10 terms of the AP 10, 11, 12, …? (a) 290 (b) 19 (c) 145 (d) 150
  4. 4.What is the 35th term of the AP 11, 15, 19, 23, …? (a) 136 (b) 151 (c) 140 (d) 147
  5. 5.What is the 33rd term of the AP 4, 8, 12, 16, …? (a) 128 (b) 133 (c) 132 (d) 136
  6. 6.What is the sum of the first 10 terms of the AP 8, 10, 12, …? (a) 26 (b) 340 (c) 180 (d) 170
  7. 7.What is the sum of the first 12 terms of the AP 6, 8, 10, …? (a) 216 (b) 408 (c) 204 (d) 28
  8. 8.What is the sum of the first 29 odd numbers (1 + 3 + 5 + …)? (a) 435 (b) 870 (c) 841 (d) 57
  9. 9.What is the 29th term of the AP 9, 14, 19, 24, …? (a) 140 (b) 145 (c) 154 (d) 149
  10. 10.What is the 21st term of the AP 1, 5, 9, 13, …? (a) 85 (b) 80 (c) 84 (d) 81
  11. 11.What is the sum of all the whole numbers from 1 to 80? (a) 6480 (b) 3240 (c) 3160 (d) 3200
  12. 12.What is the sum of the first 18 odd numbers (1 + 3 + 5 + …)? (a) 171 (b) 342 (c) 35 (d) 324
  13. 13.What is the sum of the first 20 odd numbers (1 + 3 + 5 + …)? (a) 210 (b) 39 (c) 400 (d) 420
  14. 14.What is the sum of the first 9 terms of the AP 9, 15, 21, …? (a) 57 (b) 594 (c) 297 (d) 324
  15. 15.Which term of the AP 8, 14, 20, 26, … is 188? (a) 32nd (b) 30th (c) 33rd (d) 31st
  16. 16.What is the 36th term of the AP 5, 14, 23, 32, …? (a) 320 (b) 329 (c) 315 (d) 324
  17. 17.What is the missing term in the AP 10, ?, 26, 34, 42? (a) 18 (b) 17 (c) 26 (d) 19
  18. 18.What is the 13th term of the AP 10, 13, 16, 19, …? (a) 39 (b) 36 (c) 49 (d) 46
  19. 19.What is the sum of the first 21 odd numbers (1 + 3 + 5 + …)? (a) 441 (b) 41 (c) 462 (d) 231
  20. 20.What is the missing term in the AP 8, 15, 22, ?, 36? (a) 29 (b) 36 (c) 28 (d) 30
  21. 21.Which term of the AP 3, 8, 13, 18, … is 73? (a) 15th (b) 17th (c) 14th (d) 16th
  22. 22.What is the sum of the first 8 terms of the AP 4, 7, 10, …? (a) 25 (b) 232 (c) 128 (d) 116
  23. 23.What is the sum of the first 24 odd numbers (1 + 3 + 5 + …)? (a) 300 (b) 600 (c) 47 (d) 576
  24. 24.Which term of the AP 3, 5, 7, 9, … is 27? (a) 12th (b) 14th (c) 15th (d) 13th
  25. 25.What is the missing term in the AP 20, ?, 26, 29, 32? (a) 22 (b) 24 (c) 26 (d) 23
  26. 26.What is the 19th term of the AP 5, 12, 19, 26, …? (a) 138 (b) 133 (c) 131 (d) 126
  27. 27.What is the sum of all the whole numbers from 1 to 62? (a) 1891 (b) 1953 (c) 1922 (d) 3906
  28. 28.What is the sum of all the whole numbers from 1 to 60? (a) 3660 (b) 1830 (c) 1800 (d) 1770
  29. 29.What is the 31st term of the AP 14, 17, 20, 23, …? (a) 93 (b) 107 (c) 104 (d) 90
  30. 30.What is the 26th term of the AP 9, 17, 25, 33, …? (a) 209 (b) 200 (c) 217 (d) 208
  31. 31.What is the sum of all the whole numbers from 1 to 36? (a) 648 (b) 666 (c) 630 (d) 1332
  32. 32.What is the 19th term of the AP 4, 13, 22, 31, …? (a) 175 (b) 166 (c) 162 (d) 171
  33. 33.What is the 36th term of the AP 19, 21, 23, 25, …? (a) 72 (b) 70 (c) 89 (d) 91
  34. 34.What is the 16th term of the AP 2, 11, 20, 29, …? (a) 137 (b) 135 (c) 146 (d) 144
  35. 35.What is the sum of all the whole numbers from 1 to 56? (a) 1568 (b) 3192 (c) 1540 (d) 1596
  36. 36.What is the 36th term of the AP 12, 16, 20, 24, …? (a) 140 (b) 156 (c) 152 (d) 144
  37. 37.What is the sum of the first 6 terms of the AP 2, 8, 14, …? (a) 120 (b) 32 (c) 102 (d) 204
  38. 38.What is the 18th term of the AP 11, 17, 23, 29, …? (a) 108 (b) 102 (c) 113 (d) 119
  39. 39.What is the sum of the first 5 terms of the AP 5, 11, 17, …? (a) 85 (b) 29 (c) 100 (d) 170
  40. 40.What is the 30th term of the AP 5, 9, 13, 17, …? (a) 120 (b) 121 (c) 125 (d) 116

Answer key

  1. 8th
  2. 120
  3. 145
  4. 147
  5. 132
  6. 170
  7. 204
  8. 841
  9. 149
  10. 81
  11. 3240
  12. 324
  13. 400
  14. 297
  15. 31st
  16. 320
  17. 18
  18. 46
  19. 441
  20. 29
  21. 15th
  22. 116
  23. 576
  24. 13th
  25. 23
  26. 131
  27. 1953
  28. 1830
  29. 104
  30. 209
  31. 666
  32. 166
  33. 89
  34. 137
  35. 1596
  36. 152
  37. 102
  38. 113
  39. 85
  40. 121

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