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Arithmetic Progression Worksheet for Olympiad

Maths Olympiad topic 29: Sequences and AP · Set 832 · 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 17th term of the AP 8, 16, 24, 32, …? (a) 136 (b) 128 (c) 144 (d) 137
  2. 2.Which term of the AP 4, 7, 10, 13, … is 73? (a) 26th (b) 24th (c) 25th (d) 23rd
  3. 3.What is the missing term in the AP 4, 10, ?, 22, 28? (a) 16 (b) 17 (c) 15 (d) 22
  4. 4.What is the 31st term of the AP 4, 8, 12, 16, …? (a) 124 (b) 120 (c) 128 (d) 125
  5. 5.What is the sum of the first 17 odd numbers (1 + 3 + 5 + …)? (a) 33 (b) 153 (c) 289 (d) 306
  6. 6.What is the 35th term of the AP 2, 4, 6, 8, …? (a) 70 (b) 72 (c) 71 (d) 68
  7. 7.What is the sum of the first 21 odd numbers (1 + 3 + 5 + …)? (a) 462 (b) 41 (c) 231 (d) 441
  8. 8.What is the 27th term of the AP 12, 16, 20, 24, …? (a) 108 (b) 116 (c) 104 (d) 120
  9. 9.What is the 27th term of the AP 6, 11, 16, 21, …? (a) 141 (b) 130 (c) 136 (d) 135
  10. 10.What is the sum of the first 9 terms of the AP 9, 14, 19, …? (a) 522 (b) 261 (c) 266 (d) 49
  11. 11.What is the sum of the first 11 terms of the AP 4, 6, 8, …? (a) 24 (b) 308 (c) 165 (d) 154
  12. 12.What is the sum of the first 7 odd numbers (1 + 3 + 5 + …)? (a) 13 (b) 49 (c) 56 (d) 28
  13. 13.What is the sum of all the whole numbers from 1 to 46? (a) 1081 (b) 2162 (c) 1058 (d) 1035
  14. 14.What is the sum of the first 6 odd numbers (1 + 3 + 5 + …)? (a) 42 (b) 36 (c) 21 (d) 11
  15. 15.What is the missing term in the AP 11, 13, ?, 17, 19? (a) 16 (b) 17 (c) 14 (d) 15
  16. 16.Which term of the AP 1, 8, 15, 22, … is 92? (a) 13th (b) 16th (c) 14th (d) 15th
  17. 17.What is the 17th term of the AP 12, 20, 28, 36, …? (a) 128 (b) 136 (c) 140 (d) 148
  18. 18.What is the sum of the first 24 odd numbers (1 + 3 + 5 + …)? (a) 300 (b) 600 (c) 576 (d) 47
  19. 19.What is the 26th term of the AP 3, 10, 17, 24, …? (a) 178 (b) 182 (c) 185 (d) 175
  20. 20.What is the sum of the first 10 terms of the AP 7, 8, 9, …? (a) 120 (b) 115 (c) 230 (d) 16
  21. 21.What is the sum of all the whole numbers from 1 to 49? (a) 1176 (b) 1226 (c) 1225 (d) 2450
  22. 22.What is the sum of all the whole numbers from 1 to 86? (a) 7482 (b) 3741 (c) 3698 (d) 3655
  23. 23.What is the sum of the first 9 terms of the AP 4, 7, 10, …? (a) 147 (b) 288 (c) 28 (d) 144
  24. 24.Which term of the AP 3, 7, 11, 15, … is 155? (a) 38th (b) 41st (c) 40th (d) 39th
  25. 25.What is the 15th term of the AP 11, 16, 21, 26, …? (a) 70 (b) 81 (c) 75 (d) 86
  26. 26.What is the sum of the first 8 terms of the AP 10, 11, 12, …? (a) 108 (b) 17 (c) 112 (d) 216
  27. 27.What is the sum of the first 6 terms of the AP 6, 10, 14, …? (a) 192 (b) 96 (c) 108 (d) 26
  28. 28.What is the sum of the first 25 odd numbers (1 + 3 + 5 + …)? (a) 650 (b) 625 (c) 325 (d) 49
  29. 29.What is the sum of the first 10 terms of the AP 10, 14, 18, …? (a) 280 (b) 560 (c) 300 (d) 46
  30. 30.What is the sum of the first 10 odd numbers (1 + 3 + 5 + …)? (a) 55 (b) 110 (c) 100 (d) 19
  31. 31.Which term of the AP 12, 16, 20, 24, … is 140? (a) 33rd (b) 35th (c) 34th (d) 32nd
  32. 32.What is the sum of all the whole numbers from 1 to 79? (a) 3161 (b) 6320 (c) 3081 (d) 3160
  33. 33.What is the missing term in the AP 17, 19, 21, ?, 25? (a) 22 (b) 23 (c) 24 (d) 25
  34. 34.What is the sum of the first 10 terms of the AP 1, 7, 13, …? (a) 560 (b) 55 (c) 310 (d) 280
  35. 35.What is the sum of the first 12 terms of the AP 3, 7, 11, …? (a) 324 (b) 600 (c) 47 (d) 300
  36. 36.What is the sum of all the whole numbers from 1 to 58? (a) 1682 (b) 1653 (c) 3422 (d) 1711
  37. 37.What is the missing term in the AP 14, ?, 20, 23, 26? (a) 20 (b) 16 (c) 17 (d) 18
  38. 38.What is the sum of the first 30 odd numbers (1 + 3 + 5 + …)? (a) 59 (b) 465 (c) 930 (d) 900
  39. 39.What is the 36th term of the AP 11, 15, 19, 23, …? (a) 144 (b) 140 (c) 155 (d) 151
  40. 40.What is the missing term in the AP 8, ?, 20, 26, 32? (a) 20 (b) 15 (c) 13 (d) 14

Answer key

  1. 136
  2. 24th
  3. 16
  4. 124
  5. 289
  6. 70
  7. 441
  8. 116
  9. 136
  10. 261
  11. 154
  12. 49
  13. 1081
  14. 36
  15. 15
  16. 14th
  17. 140
  18. 576
  19. 178
  20. 115
  21. 1225
  22. 3741
  23. 144
  24. 39th
  25. 81
  26. 108
  27. 96
  28. 625
  29. 280
  30. 100
  31. 33rd
  32. 3160
  33. 23
  34. 280
  35. 300
  36. 1711
  37. 17
  38. 900
  39. 151
  40. 14

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