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Arithmetic Progression Worksheet for Olympiad

Maths Olympiad topic 29: Sequences and AP · Set 365 · 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 missing term in the AP 5, 10, 15, ?, 25? (a) 19 (b) 21 (c) 20 (d) 25
  2. 2.What is the sum of the first 9 terms of the AP 2, 7, 12, …? (a) 396 (b) 198 (c) 42 (d) 203
  3. 3.What is the missing term in the AP 19, 22, ?, 28, 31? (a) 26 (b) 25 (c) 24 (d) 28
  4. 4.What is the sum of the first 21 odd numbers (1 + 3 + 5 + …)? (a) 441 (b) 462 (c) 41 (d) 231
  5. 5.What is the sum of the first 8 terms of the AP 7, 13, 19, …? (a) 49 (b) 248 (c) 224 (d) 448
  6. 6.Which term of the AP 5, 13, 21, 29, … is 85? (a) 13th (b) 11th (c) 10th (d) 12th
  7. 7.What is the sum of the first 12 terms of the AP 2, 3, 4, …? (a) 90 (b) 96 (c) 13 (d) 180
  8. 8.What is the 30th term of the AP 19, 25, 31, 37, …? (a) 193 (b) 174 (c) 180 (d) 199
  9. 9.What is the missing term in the AP 7, 9, 11, ?, 15? (a) 14 (b) 13 (c) 15 (d) 12
  10. 10.What is the sum of the first 20 odd numbers (1 + 3 + 5 + …)? (a) 210 (b) 420 (c) 39 (d) 400
  11. 11.What is the sum of all the whole numbers from 1 to 33? (a) 528 (b) 561 (c) 562 (d) 1122
  12. 12.Which term of the AP 11, 14, 17, 20, … is 92? (a) 29th (b) 28th (c) 30th (d) 27th
  13. 13.What is the 40th term of the AP 6, 8, 10, 12, …? (a) 78 (b) 80 (c) 86 (d) 84
  14. 14.Which term of the AP 9, 12, 15, 18, … is 54? (a) 17th (b) 16th (c) 18th (d) 15th
  15. 15.Which term of the AP 16, 19, 22, 25, … is 94? (a) 28th (b) 26th (c) 29th (d) 27th
  16. 16.What is the sum of all the whole numbers from 1 to 97? (a) 9506 (b) 4656 (c) 4753 (d) 4754
  17. 17.What is the missing term in the AP 15, 17, ?, 21, 23? (a) 21 (b) 19 (c) 18 (d) 20
  18. 18.What is the missing term in the AP 5, 13, 21, ?, 37? (a) 37 (b) 28 (c) 30 (d) 29
  19. 19.What is the sum of the first 5 terms of the AP 4, 6, 8, …? (a) 40 (b) 12 (c) 80 (d) 45
  20. 20.What is the 21st term of the AP 12, 19, 26, 33, …? (a) 140 (b) 152 (c) 147 (d) 159
  21. 21.What is the sum of the first 10 terms of the AP 1, 2, 3, …? (a) 10 (b) 60 (c) 55 (d) 110
  22. 22.What is the sum of all the whole numbers from 1 to 54? (a) 1458 (b) 1485 (c) 2970 (d) 1431
  23. 23.What is the missing term in the AP 18, ?, 34, 42, 50? (a) 34 (b) 25 (c) 27 (d) 26
  24. 24.What is the sum of all the whole numbers from 1 to 84? (a) 3486 (b) 3570 (c) 3528 (d) 7140
  25. 25.What is the 13th term of the AP 2, 10, 18, 26, …? (a) 106 (b) 98 (c) 96 (d) 104
  26. 26.Which term of the AP 9, 15, 21, 27, … is 243? (a) 41st (b) 40th (c) 42nd (d) 39th
  27. 27.Which term of the AP 5, 13, 21, 29, … is 157? (a) 21st (b) 19th (c) 20th (d) 22nd
  28. 28.What is the sum of the first 10 terms of the AP 8, 11, 14, …? (a) 430 (b) 230 (c) 35 (d) 215
  29. 29.What is the sum of the first 6 terms of the AP 1, 4, 7, …? (a) 16 (b) 102 (c) 60 (d) 51
  30. 30.What is the sum of the first 9 odd numbers (1 + 3 + 5 + …)? (a) 45 (b) 17 (c) 90 (d) 81
  31. 31.What is the sum of all the whole numbers from 1 to 22? (a) 242 (b) 506 (c) 253 (d) 231
  32. 32.What is the sum of all the whole numbers from 1 to 75? (a) 2851 (b) 5700 (c) 2850 (d) 2775
  33. 33.What is the sum of the first 24 odd numbers (1 + 3 + 5 + …)? (a) 47 (b) 600 (c) 300 (d) 576
  34. 34.What is the 35th term of the AP 3, 5, 7, 9, …? (a) 73 (b) 71 (c) 70 (d) 68
  35. 35.What is the sum of the first 15 odd numbers (1 + 3 + 5 + …)? (a) 225 (b) 240 (c) 29 (d) 120
  36. 36.What is the sum of the first 9 terms of the AP 4, 8, 12, …? (a) 360 (b) 198 (c) 180 (d) 36
  37. 37.What is the sum of all the whole numbers from 1 to 55? (a) 1541 (b) 1485 (c) 3080 (d) 1540
  38. 38.What is the 38th term of the AP 14, 21, 28, 35, …? (a) 280 (b) 266 (c) 259 (d) 273
  39. 39.What is the sum of the first 30 odd numbers (1 + 3 + 5 + …)? (a) 465 (b) 59 (c) 930 (d) 900
  40. 40.What is the sum of all the whole numbers from 1 to 95? (a) 4561 (b) 4465 (c) 4560 (d) 9120

Answer key

  1. 20
  2. 198
  3. 25
  4. 441
  5. 224
  6. 11th
  7. 90
  8. 193
  9. 13
  10. 400
  11. 561
  12. 28th
  13. 84
  14. 16th
  15. 27th
  16. 4753
  17. 19
  18. 29
  19. 40
  20. 152
  21. 55
  22. 1485
  23. 26
  24. 3570
  25. 98
  26. 40th
  27. 20th
  28. 215
  29. 51
  30. 81
  31. 253
  32. 2850
  33. 576
  34. 71
  35. 225
  36. 180
  37. 1540
  38. 273
  39. 900
  40. 4560

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