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Arithmetic Progression Worksheet for Olympiad

Maths Olympiad topic 29: Sequences and AP · Set 250 · 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 18th term of the AP 18, 27, 36, 45, …? (a) 153 (b) 171 (c) 162 (d) 180
  2. 2.What is the sum of all the whole numbers from 1 to 96? (a) 4560 (b) 4656 (c) 4608 (d) 9312
  3. 3.What is the sum of the first 11 terms of the AP 4, 7, 10, …? (a) 209 (b) 418 (c) 212 (d) 34
  4. 4.What is the sum of the first 6 terms of the AP 2, 8, 14, …? (a) 120 (b) 204 (c) 32 (d) 102
  5. 5.What is the 14th term of the AP 8, 10, 12, 14, …? (a) 26 (b) 28 (c) 36 (d) 34
  6. 6.What is the sum of the first 5 odd numbers (1 + 3 + 5 + …)? (a) 15 (b) 30 (c) 25 (d) 9
  7. 7.Which term of the AP 2, 4, 6, 8, … is 30? (a) 14th (b) 16th (c) 15th (d) 17th
  8. 8.Which term of the AP 9, 14, 19, 24, … is 94? (a) 19th (b) 20th (c) 18th (d) 17th
  9. 9.Which term of the AP 15, 22, 29, 36, … is 134? (a) 17th (b) 18th (c) 20th (d) 19th
  10. 10.What is the 14th term of the AP 14, 20, 26, 32, …? (a) 92 (b) 78 (c) 84 (d) 98
  11. 11.What is the sum of the first 15 odd numbers (1 + 3 + 5 + …)? (a) 225 (b) 240 (c) 29 (d) 120
  12. 12.What is the sum of the first 11 terms of the AP 5, 7, 9, …? (a) 25 (b) 330 (c) 176 (d) 165
  13. 13.What is the missing term in the AP 9, ?, 15, 18, 21? (a) 13 (b) 15 (c) 11 (d) 12
  14. 14.What is the missing term in the AP 19, 22, ?, 28, 31? (a) 24 (b) 26 (c) 28 (d) 25
  15. 15.What is the sum of the first 22 odd numbers (1 + 3 + 5 + …)? (a) 43 (b) 253 (c) 506 (d) 484
  16. 16.What is the sum of the first 6 terms of the AP 3, 8, 13, …? (a) 186 (b) 28 (c) 108 (d) 93
  17. 17.What is the missing term in the AP 5, ?, 17, 23, 29? (a) 17 (b) 11 (c) 12 (d) 10
  18. 18.What is the 16th term of the AP 15, 21, 27, 33, …? (a) 111 (b) 90 (c) 96 (d) 105
  19. 19.What is the sum of the first 11 terms of the AP 4, 8, 12, …? (a) 286 (b) 264 (c) 528 (d) 44
  20. 20.What is the sum of all the whole numbers from 1 to 36? (a) 666 (b) 630 (c) 1332 (d) 648
  21. 21.What is the sum of all the whole numbers from 1 to 71? (a) 2556 (b) 5112 (c) 2557 (d) 2485
  22. 22.What is the sum of all the whole numbers from 1 to 59? (a) 1711 (b) 3540 (c) 1770 (d) 1771
  23. 23.What is the sum of the first 12 odd numbers (1 + 3 + 5 + …)? (a) 156 (b) 144 (c) 23 (d) 78
  24. 24.What is the missing term in the AP 16, 18, ?, 22, 24? (a) 21 (b) 19 (c) 22 (d) 20
  25. 25.What is the sum of the first 6 terms of the AP 4, 6, 8, …? (a) 108 (b) 14 (c) 54 (d) 60
  26. 26.What is the missing term in the AP 4, ?, 8, 10, 12? (a) 7 (b) 6 (c) 8 (d) 5
  27. 27.What is the sum of all the whole numbers from 1 to 83? (a) 3487 (b) 3486 (c) 6972 (d) 3403
  28. 28.What is the sum of the first 8 terms of the AP 10, 13, 16, …? (a) 328 (b) 176 (c) 31 (d) 164
  29. 29.What is the sum of all the whole numbers from 1 to 50? (a) 1225 (b) 2550 (c) 1275 (d) 1250
  30. 30.What is the sum of the first 10 terms of the AP 10, 13, 16, …? (a) 37 (b) 250 (c) 470 (d) 235
  31. 31.Which term of the AP 8, 16, 24, 32, … is 224? (a) 27th (b) 28th (c) 29th (d) 30th
  32. 32.What is the 37th term of the AP 16, 20, 24, 28, …? (a) 164 (b) 148 (c) 160 (d) 144
  33. 33.What is the 16th term of the AP 19, 26, 33, 40, …? (a) 105 (b) 112 (c) 124 (d) 131
  34. 34.What is the sum of the first 17 odd numbers (1 + 3 + 5 + …)? (a) 33 (b) 289 (c) 306 (d) 153
  35. 35.What is the 33rd term of the AP 7, 15, 23, 31, …? (a) 271 (b) 256 (c) 263 (d) 264
  36. 36.Which term of the AP 1, 3, 5, 7, … is 35? (a) 19th (b) 18th (c) 20th (d) 17th
  37. 37.What is the sum of the first 7 terms of the AP 2, 8, 14, …? (a) 280 (b) 161 (c) 140 (d) 38
  38. 38.What is the 16th term of the AP 15, 24, 33, 42, …? (a) 144 (b) 135 (c) 159 (d) 150
  39. 39.What is the sum of the first 8 terms of the AP 2, 3, 4, …? (a) 9 (b) 88 (c) 44 (d) 48
  40. 40.Which term of the AP 3, 12, 21, 30, … is 165? (a) 18th (b) 20th (c) 19th (d) 21st

Answer key

  1. 171
  2. 4656
  3. 209
  4. 102
  5. 34
  6. 25
  7. 15th
  8. 18th
  9. 18th
  10. 92
  11. 225
  12. 165
  13. 12
  14. 25
  15. 484
  16. 93
  17. 11
  18. 105
  19. 264
  20. 666
  21. 2556
  22. 1770
  23. 144
  24. 20
  25. 54
  26. 6
  27. 3486
  28. 164
  29. 1275
  30. 235
  31. 28th
  32. 160
  33. 124
  34. 289
  35. 263
  36. 18th
  37. 140
  38. 150
  39. 44
  40. 19th

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