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Arithmetic Progression Worksheet for Olympiad

Maths Olympiad topic 29: Sequences and AP · Set 524 · 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 60? (a) 3660 (b) 1770 (c) 1800 (d) 1830
  2. 2.What is the missing term in the AP 3, ?, 21, 30, 39? (a) 21 (b) 11 (c) 13 (d) 12
  3. 3.What is the missing term in the AP 15, 24, 33, ?, 51? (a) 43 (b) 42 (c) 51 (d) 41
  4. 4.Which term of the AP 4, 10, 16, 22, … is 118? (a) 19th (b) 20th (c) 22nd (d) 21st
  5. 5.What is the sum of the first 21 odd numbers (1 + 3 + 5 + …)? (a) 231 (b) 462 (c) 441 (d) 41
  6. 6.What is the sum of the first 6 terms of the AP 2, 6, 10, …? (a) 84 (b) 72 (c) 22 (d) 144
  7. 7.What is the 22nd term of the AP 17, 24, 31, 38, …? (a) 164 (b) 171 (c) 147 (d) 154
  8. 8.What is the sum of all the whole numbers from 1 to 58? (a) 1653 (b) 3422 (c) 1682 (d) 1711
  9. 9.What is the sum of the first 7 terms of the AP 10, 14, 18, …? (a) 308 (b) 34 (c) 168 (d) 154
  10. 10.What is the sum of the first 10 terms of the AP 10, 11, 12, …? (a) 145 (b) 290 (c) 19 (d) 150
  11. 11.Which term of the AP 8, 15, 22, 29, … is 92? (a) 14th (b) 12th (c) 15th (d) 13th
  12. 12.What is the sum of all the whole numbers from 1 to 97? (a) 9506 (b) 4656 (c) 4754 (d) 4753
  13. 13.What is the 31st term of the AP 10, 14, 18, 22, …? (a) 124 (b) 134 (c) 120 (d) 130
  14. 14.What is the 11th term of the AP 2, 6, 10, 14, …? (a) 44 (b) 42 (c) 40 (d) 46
  15. 15.What is the sum of all the whole numbers from 1 to 100? (a) 10100 (b) 5000 (c) 4950 (d) 5050
  16. 16.What is the sum of the first 11 odd numbers (1 + 3 + 5 + …)? (a) 21 (b) 66 (c) 121 (d) 132
  17. 17.What is the 19th term of the AP 13, 16, 19, 22, …? (a) 57 (b) 67 (c) 70 (d) 54
  18. 18.What is the 38th term of the AP 13, 16, 19, 22, …? (a) 127 (b) 111 (c) 124 (d) 114
  19. 19.What is the sum of the first 6 terms of the AP 1, 2, 3, …? (a) 24 (b) 21 (c) 6 (d) 42
  20. 20.What is the 38th term of the AP 15, 17, 19, 21, …? (a) 91 (b) 76 (c) 89 (d) 74
  21. 21.What is the sum of the first 5 terms of the AP 9, 15, 21, …? (a) 33 (b) 105 (c) 210 (d) 120
  22. 22.What is the 18th term of the AP 2, 8, 14, 20, …? (a) 110 (b) 102 (c) 108 (d) 104
  23. 23.What is the sum of the first 23 odd numbers (1 + 3 + 5 + …)? (a) 529 (b) 45 (c) 552 (d) 276
  24. 24.What is the sum of the first 8 terms of the AP 6, 10, 14, …? (a) 320 (b) 34 (c) 160 (d) 176
  25. 25.What is the 34th term of the AP 18, 22, 26, 30, …? (a) 154 (b) 132 (c) 150 (d) 136
  26. 26.What is the missing term in the AP 17, 20, ?, 26, 29? (a) 24 (b) 26 (c) 22 (d) 23
  27. 27.What is the sum of all the whole numbers from 1 to 28? (a) 392 (b) 406 (c) 378 (d) 812
  28. 28.What is the 32nd term of the AP 9, 16, 23, 30, …? (a) 217 (b) 224 (c) 233 (d) 226
  29. 29.What is the sum of all the whole numbers from 1 to 70? (a) 2450 (b) 2485 (c) 2415 (d) 4970
  30. 30.What is the 14th term of the AP 5, 11, 17, 23, …? (a) 89 (b) 83 (c) 78 (d) 84
  31. 31.What is the 28th term of the AP 1, 6, 11, 16, …? (a) 141 (b) 140 (c) 136 (d) 135
  32. 32.Which term of the AP 1, 4, 7, 10, … is 64? (a) 23rd (b) 24th (c) 21st (d) 22nd
  33. 33.Which term of the AP 9, 18, 27, 36, … is 126? (a) 16th (b) 14th (c) 13th (d) 15th
  34. 34.What is the sum of the first 9 odd numbers (1 + 3 + 5 + …)? (a) 17 (b) 90 (c) 81 (d) 45
  35. 35.Which term of the AP 17, 23, 29, 35, … is 89? (a) 14th (b) 15th (c) 12th (d) 13th
  36. 36.What is the sum of the first 12 terms of the AP 8, 14, 20, …? (a) 984 (b) 492 (c) 528 (d) 74
  37. 37.What is the 26th term of the AP 4, 11, 18, 25, …? (a) 182 (b) 186 (c) 175 (d) 179
  38. 38.What is the sum of the first 7 terms of the AP 2, 6, 10, …? (a) 26 (b) 98 (c) 112 (d) 196
  39. 39.What is the sum of the first 11 terms of the AP 5, 6, 7, …? (a) 15 (b) 111 (c) 220 (d) 110
  40. 40.What is the sum of all the whole numbers from 1 to 92? (a) 4232 (b) 4278 (c) 8556 (d) 4186

Answer key

  1. 1830
  2. 12
  3. 42
  4. 20th
  5. 441
  6. 72
  7. 164
  8. 1711
  9. 154
  10. 145
  11. 13th
  12. 4753
  13. 130
  14. 42
  15. 5050
  16. 121
  17. 67
  18. 124
  19. 21
  20. 89
  21. 105
  22. 104
  23. 529
  24. 160
  25. 150
  26. 23
  27. 406
  28. 226
  29. 2485
  30. 83
  31. 136
  32. 22nd
  33. 14th
  34. 81
  35. 13th
  36. 492
  37. 179
  38. 98
  39. 110
  40. 4278

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