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Arithmetic Progression Worksheet for Olympiad

Maths Olympiad topic 29: Sequences and AP · Set 653 · 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 the first 7 terms of the AP 5, 6, 7, …? (a) 11 (b) 57 (c) 56 (d) 112
  2. 2.What is the sum of all the whole numbers from 1 to 70? (a) 2485 (b) 4970 (c) 2415 (d) 2450
  3. 3.What is the 13th term of the AP 18, 24, 30, 36, …? (a) 90 (b) 96 (c) 78 (d) 72
  4. 4.Which term of the AP 15, 18, 21, 24, … is 129? (a) 43rd (b) 39th (c) 38th (d) 40th
  5. 5.What is the 25th term of the AP 6, 12, 18, 24, …? (a) 156 (b) 144 (c) 151 (d) 150
  6. 6.What is the sum of all the whole numbers from 1 to 44? (a) 946 (b) 1980 (c) 968 (d) 990
  7. 7.What is the missing term in the AP 5, ?, 21, 29, 37? (a) 13 (b) 14 (c) 12 (d) 21
  8. 8.What is the 37th term of the AP 12, 15, 18, 21, …? (a) 120 (b) 108 (c) 123 (d) 111
  9. 9.What is the sum of the first 6 terms of the AP 6, 8, 10, …? (a) 66 (b) 72 (c) 132 (d) 16
  10. 10.What is the missing term in the AP 17, ?, 23, 26, 29? (a) 23 (b) 19 (c) 20 (d) 21
  11. 11.What is the sum of all the whole numbers from 1 to 21? (a) 210 (b) 462 (c) 232 (d) 231
  12. 12.What is the sum of the first 5 terms of the AP 1, 6, 11, …? (a) 55 (b) 110 (c) 60 (d) 21
  13. 13.What is the 34th term of the AP 10, 16, 22, 28, …? (a) 214 (b) 208 (c) 204 (d) 198
  14. 14.What is the sum of the first 6 odd numbers (1 + 3 + 5 + …)? (a) 11 (b) 42 (c) 21 (d) 36
  15. 15.What is the sum of the first 6 terms of the AP 2, 7, 12, …? (a) 174 (b) 102 (c) 87 (d) 27
  16. 16.What is the sum of the first 9 terms of the AP 8, 11, 14, …? (a) 32 (b) 180 (c) 183 (d) 360
  17. 17.What is the sum of all the whole numbers from 1 to 25? (a) 650 (b) 326 (c) 300 (d) 325
  18. 18.What is the 17th term of the AP 2, 7, 12, 17, …? (a) 87 (b) 80 (c) 82 (d) 85
  19. 19.What is the missing term in the AP 8, ?, 18, 23, 28? (a) 18 (b) 12 (c) 13 (d) 14
  20. 20.What is the 25th term of the AP 2, 7, 12, 17, …? (a) 127 (b) 120 (c) 122 (d) 125
  21. 21.What is the 38th term of the AP 10, 16, 22, 28, …? (a) 232 (b) 238 (c) 222 (d) 228
  22. 22.What is the missing term in the AP 7, 12, ?, 22, 27? (a) 16 (b) 22 (c) 17 (d) 18
  23. 23.What is the sum of all the whole numbers from 1 to 73? (a) 2702 (b) 2701 (c) 5402 (d) 2628
  24. 24.What is the sum of the first 21 odd numbers (1 + 3 + 5 + …)? (a) 231 (b) 441 (c) 462 (d) 41
  25. 25.Which term of the AP 8, 14, 20, 26, … is 176? (a) 30th (b) 28th (c) 31st (d) 29th
  26. 26.What is the 25th term of the AP 1, 8, 15, 22, …? (a) 176 (b) 168 (c) 175 (d) 169
  27. 27.What is the missing term in the AP 20, 25, ?, 35, 40? (a) 29 (b) 30 (c) 31 (d) 35
  28. 28.What is the 11th term of the AP 12, 16, 20, 24, …? (a) 52 (b) 40 (c) 44 (d) 56
  29. 29.What is the sum of the first 10 terms of the AP 7, 13, 19, …? (a) 370 (b) 340 (c) 61 (d) 680
  30. 30.What is the 26th term of the AP 12, 16, 20, 24, …? (a) 104 (b) 112 (c) 116 (d) 100
  31. 31.What is the 24th term of the AP 14, 23, 32, 41, …? (a) 207 (b) 230 (c) 216 (d) 221
  32. 32.What is the sum of the first 5 terms of the AP 5, 6, 7, …? (a) 70 (b) 36 (c) 9 (d) 35
  33. 33.What is the 33rd term of the AP 10, 17, 24, 31, …? (a) 241 (b) 224 (c) 234 (d) 231
  34. 34.What is the sum of the first 7 odd numbers (1 + 3 + 5 + …)? (a) 56 (b) 13 (c) 28 (d) 49
  35. 35.What is the 16th term of the AP 19, 25, 31, 37, …? (a) 90 (b) 96 (c) 109 (d) 115
  36. 36.What is the 27th term of the AP 11, 14, 17, 20, …? (a) 81 (b) 78 (c) 89 (d) 92
  37. 37.What is the missing term in the AP 13, 22, ?, 40, 49? (a) 32 (b) 30 (c) 40 (d) 31
  38. 38.What is the sum of the first 8 terms of the AP 8, 9, 10, …? (a) 92 (b) 184 (c) 15 (d) 96
  39. 39.What is the sum of all the whole numbers from 1 to 54? (a) 1485 (b) 1458 (c) 2970 (d) 1431
  40. 40.What is the sum of all the whole numbers from 1 to 62? (a) 1891 (b) 3906 (c) 1953 (d) 1922

Answer key

  1. 56
  2. 2485
  3. 90
  4. 39th
  5. 150
  6. 990
  7. 13
  8. 120
  9. 66
  10. 20
  11. 231
  12. 55
  13. 208
  14. 36
  15. 87
  16. 180
  17. 325
  18. 82
  19. 13
  20. 122
  21. 232
  22. 17
  23. 2701
  24. 441
  25. 29th
  26. 169
  27. 30
  28. 52
  29. 340
  30. 112
  31. 221
  32. 35
  33. 234
  34. 49
  35. 109
  36. 89
  37. 31
  38. 92
  39. 1485
  40. 1953

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