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Arithmetic Progression Worksheet for Olympiad

Maths Olympiad topic 29: Sequences and AP · Set 526 · 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 31st term of the AP 1, 3, 5, 7, …? (a) 63 (b) 62 (c) 61 (d) 60
  2. 2.What is the 13th term of the AP 17, 23, 29, 35, …? (a) 89 (b) 72 (c) 78 (d) 95
  3. 3.What is the 29th term of the AP 20, 26, 32, 38, …? (a) 168 (b) 188 (c) 174 (d) 194
  4. 4.Which term of the AP 1, 4, 7, 10, … is 70? (a) 26th (b) 24th (c) 23rd (d) 25th
  5. 5.What is the 17th term of the AP 17, 24, 31, 38, …? (a) 136 (b) 129 (c) 112 (d) 119
  6. 6.What is the sum of the first 7 terms of the AP 3, 4, 5, …? (a) 84 (b) 9 (c) 42 (d) 43
  7. 7.What is the sum of the first 8 terms of the AP 2, 6, 10, …? (a) 30 (b) 256 (c) 128 (d) 144
  8. 8.What is the sum of the first 9 terms of the AP 9, 14, 19, …? (a) 522 (b) 49 (c) 261 (d) 266
  9. 9.What is the 14th term of the AP 18, 24, 30, 36, …? (a) 78 (b) 102 (c) 96 (d) 84
  10. 10.What is the sum of the first 6 terms of the AP 8, 9, 10, …? (a) 63 (b) 13 (c) 66 (d) 126
  11. 11.What is the sum of all the whole numbers from 1 to 55? (a) 1541 (b) 3080 (c) 1485 (d) 1540
  12. 12.Which term of the AP 20, 27, 34, 41, … is 153? (a) 21st (b) 22nd (c) 20th (d) 19th
  13. 13.What is the sum of all the whole numbers from 1 to 71? (a) 2485 (b) 5112 (c) 2556 (d) 2557
  14. 14.What is the 18th term of the AP 3, 10, 17, 24, …? (a) 122 (b) 129 (c) 126 (d) 119
  15. 15.What is the sum of the first 12 terms of the AP 3, 6, 9, …? (a) 468 (b) 252 (c) 36 (d) 234
  16. 16.What is the 25th term of the AP 2, 9, 16, 23, …? (a) 177 (b) 175 (c) 170 (d) 168
  17. 17.What is the 39th term of the AP 4, 8, 12, 16, …? (a) 152 (b) 157 (c) 156 (d) 160
  18. 18.What is the missing term in the AP 2, ?, 12, 17, 22? (a) 6 (b) 8 (c) 12 (d) 7
  19. 19.Which term of the AP 9, 18, 27, 36, … is 90? (a) 9th (b) 11th (c) 10th (d) 12th
  20. 20.What is the 15th term of the AP 19, 21, 23, 25, …? (a) 30 (b) 49 (c) 47 (d) 28
  21. 21.What is the missing term in the AP 13, ?, 23, 28, 33? (a) 23 (b) 19 (c) 17 (d) 18
  22. 22.Which term of the AP 5, 7, 9, 11, … is 31? (a) 16th (b) 15th (c) 14th (d) 13th
  23. 23.What is the sum of the first 7 terms of the AP 1, 2, 3, …? (a) 28 (b) 56 (c) 7 (d) 29
  24. 24.What is the sum of all the whole numbers from 1 to 74? (a) 2738 (b) 2701 (c) 5550 (d) 2775
  25. 25.What is the sum of the first 12 terms of the AP 5, 11, 17, …? (a) 71 (b) 492 (c) 456 (d) 912
  26. 26.What is the sum of the first 12 terms of the AP 2, 7, 12, …? (a) 708 (b) 354 (c) 384 (d) 57
  27. 27.What is the 34th term of the AP 18, 22, 26, 30, …? (a) 136 (b) 132 (c) 150 (d) 154
  28. 28.What is the missing term in the AP 12, 14, 16, ?, 20? (a) 20 (b) 19 (c) 17 (d) 18
  29. 29.What is the 29th term of the AP 10, 13, 16, 19, …? (a) 94 (b) 84 (c) 97 (d) 87
  30. 30.What is the 23rd term of the AP 2, 9, 16, 23, …? (a) 163 (b) 156 (c) 161 (d) 154
  31. 31.What is the 24th term of the AP 2, 9, 16, 23, …? (a) 161 (b) 163 (c) 170 (d) 168
  32. 32.What is the sum of the first 12 terms of the AP 8, 10, 12, …? (a) 30 (b) 228 (c) 456 (d) 240
  33. 33.What is the sum of the first 11 odd numbers (1 + 3 + 5 + …)? (a) 121 (b) 66 (c) 132 (d) 21
  34. 34.What is the sum of the first 6 terms of the AP 6, 10, 14, …? (a) 26 (b) 108 (c) 96 (d) 192
  35. 35.What is the sum of all the whole numbers from 1 to 59? (a) 1711 (b) 1771 (c) 1770 (d) 3540
  36. 36.What is the missing term in the AP 16, ?, 34, 43, 52? (a) 25 (b) 24 (c) 26 (d) 34
  37. 37.What is the 33rd term of the AP 16, 19, 22, 25, …? (a) 96 (b) 99 (c) 112 (d) 115
  38. 38.What is the 21st term of the AP 8, 10, 12, 14, …? (a) 42 (b) 48 (c) 40 (d) 50
  39. 39.What is the missing term in the AP 5, 11, ?, 23, 29? (a) 23 (b) 16 (c) 17 (d) 18
  40. 40.What is the 18th term of the AP 17, 26, 35, 44, …? (a) 153 (b) 162 (c) 170 (d) 179

Answer key

  1. 61
  2. 89
  3. 188
  4. 24th
  5. 129
  6. 42
  7. 128
  8. 261
  9. 96
  10. 63
  11. 1540
  12. 20th
  13. 2556
  14. 122
  15. 234
  16. 170
  17. 156
  18. 7
  19. 10th
  20. 47
  21. 18
  22. 14th
  23. 28
  24. 2775
  25. 456
  26. 354
  27. 150
  28. 18
  29. 94
  30. 156
  31. 163
  32. 228
  33. 121
  34. 96
  35. 1770
  36. 25
  37. 112
  38. 48
  39. 17
  40. 170

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