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Arithmetic Progression Worksheet for Olympiad

Maths Olympiad topic 29: Sequences and AP · Set 611 · 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 34th term of the AP 12, 15, 18, 21, …? (a) 99 (b) 102 (c) 111 (d) 114
  2. 2.What is the 32nd term of the AP 3, 11, 19, 27, …? (a) 251 (b) 256 (c) 248 (d) 259
  3. 3.What is the sum of the first 6 terms of the AP 7, 9, 11, …? (a) 78 (b) 144 (c) 17 (d) 72
  4. 4.What is the 15th term of the AP 13, 21, 29, 37, …? (a) 112 (b) 125 (c) 133 (d) 120
  5. 5.Which term of the AP 16, 24, 32, 40, … is 224? (a) 28th (b) 29th (c) 27th (d) 26th
  6. 6.What is the sum of the first 10 terms of the AP 3, 6, 9, …? (a) 330 (b) 30 (c) 180 (d) 165
  7. 7.Which term of the AP 15, 24, 33, 42, … is 276? (a) 30th (b) 31st (c) 29th (d) 32nd
  8. 8.What is the sum of all the whole numbers from 1 to 77? (a) 3003 (b) 2926 (c) 6006 (d) 3004
  9. 9.What is the missing term in the AP 5, 11, 17, ?, 29? (a) 24 (b) 29 (c) 22 (d) 23
  10. 10.What is the 26th term of the AP 17, 25, 33, 41, …? (a) 225 (b) 217 (c) 200 (d) 208
  11. 11.What is the sum of the first 10 terms of the AP 1, 6, 11, …? (a) 260 (b) 46 (c) 235 (d) 470
  12. 12.What is the sum of all the whole numbers from 1 to 58? (a) 3422 (b) 1653 (c) 1682 (d) 1711
  13. 13.What is the sum of all the whole numbers from 1 to 53? (a) 1431 (b) 1432 (c) 1378 (d) 2862
  14. 14.Which term of the AP 9, 12, 15, 18, … is 51? (a) 17th (b) 15th (c) 16th (d) 14th
  15. 15.What is the missing term in the AP 9, 16, ?, 30, 37? (a) 30 (b) 23 (c) 22 (d) 24
  16. 16.Which term of the AP 4, 12, 20, 28, … is 196? (a) 27th (b) 24th (c) 26th (d) 25th
  17. 17.Which term of the AP 1, 6, 11, 16, … is 86? (a) 19th (b) 17th (c) 18th (d) 20th
  18. 18.What is the sum of the first 8 terms of the AP 6, 10, 14, …? (a) 160 (b) 34 (c) 176 (d) 320
  19. 19.Which term of the AP 17, 23, 29, 35, … is 89? (a) 13th (b) 12th (c) 14th (d) 15th
  20. 20.What is the sum of the first 10 terms of the AP 7, 13, 19, …? (a) 370 (b) 61 (c) 340 (d) 680
  21. 21.What is the sum of the first 18 odd numbers (1 + 3 + 5 + …)? (a) 35 (b) 342 (c) 171 (d) 324
  22. 22.What is the 10th term of the AP 9, 11, 13, 15, …? (a) 18 (b) 29 (c) 20 (d) 27
  23. 23.What is the sum of the first 11 terms of the AP 10, 12, 14, …? (a) 440 (b) 30 (c) 220 (d) 231
  24. 24.What is the 32nd term of the AP 18, 21, 24, 27, …? (a) 96 (b) 114 (c) 111 (d) 93
  25. 25.What is the 10th term of the AP 5, 8, 11, 14, …? (a) 32 (b) 35 (c) 27 (d) 30
  26. 26.What is the sum of the first 5 terms of the AP 4, 5, 6, …? (a) 30 (b) 8 (c) 60 (d) 31
  27. 27.What is the sum of the first 9 terms of the AP 1, 6, 11, …? (a) 194 (b) 189 (c) 41 (d) 378
  28. 28.What is the sum of the first 5 terms of the AP 4, 6, 8, …? (a) 40 (b) 12 (c) 45 (d) 80
  29. 29.Which term of the AP 4, 7, 10, 13, … is 115? (a) 40th (b) 39th (c) 37th (d) 38th
  30. 30.What is the sum of the first 12 terms of the AP 1, 3, 5, …? (a) 288 (b) 23 (c) 156 (d) 144
  31. 31.What is the 12th term of the AP 6, 12, 18, 24, …? (a) 72 (b) 78 (c) 73 (d) 66
  32. 32.What is the 38th term of the AP 3, 9, 15, 21, …? (a) 225 (b) 231 (c) 222 (d) 228
  33. 33.What is the missing term in the AP 4, 12, ?, 28, 36? (a) 21 (b) 19 (c) 28 (d) 20
  34. 34.What is the missing term in the AP 8, ?, 20, 26, 32? (a) 15 (b) 13 (c) 20 (d) 14
  35. 35.What is the sum of all the whole numbers from 1 to 97? (a) 4753 (b) 4754 (c) 4656 (d) 9506
  36. 36.What is the missing term in the AP 10, ?, 26, 34, 42? (a) 26 (b) 17 (c) 19 (d) 18
  37. 37.What is the sum of the first 11 terms of the AP 3, 7, 11, …? (a) 253 (b) 43 (c) 275 (d) 506
  38. 38.What is the 29th term of the AP 13, 16, 19, 22, …? (a) 97 (b) 84 (c) 87 (d) 100
  39. 39.What is the sum of all the whole numbers from 1 to 65? (a) 2080 (b) 4290 (c) 2146 (d) 2145
  40. 40.What is the sum of all the whole numbers from 1 to 38? (a) 741 (b) 703 (c) 1482 (d) 722

Answer key

  1. 111
  2. 251
  3. 72
  4. 125
  5. 27th
  6. 165
  7. 30th
  8. 3003
  9. 23
  10. 217
  11. 235
  12. 1711
  13. 1431
  14. 15th
  15. 23
  16. 25th
  17. 18th
  18. 160
  19. 13th
  20. 340
  21. 324
  22. 27
  23. 220
  24. 111
  25. 32
  26. 30
  27. 189
  28. 40
  29. 38th
  30. 144
  31. 72
  32. 225
  33. 20
  34. 14
  35. 4753
  36. 18
  37. 253
  38. 97
  39. 2145
  40. 741

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