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Arithmetic Progression Worksheet for Olympiad

Maths Olympiad topic 29: Sequences and AP · Set 268 · 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 10, ?, 24, 31, 38? (a) 18 (b) 16 (c) 17 (d) 24
  2. 2.What is the missing term in the AP 17, 22, ?, 32, 37? (a) 32 (b) 27 (c) 28 (d) 26
  3. 3.What is the sum of the first 9 terms of the AP 10, 13, 16, …? (a) 396 (b) 201 (c) 198 (d) 34
  4. 4.What is the sum of the first 10 terms of the AP 9, 12, 15, …? (a) 450 (b) 225 (c) 240 (d) 36
  5. 5.What is the sum of the first 11 terms of the AP 10, 15, 20, …? (a) 770 (b) 60 (c) 385 (d) 390
  6. 6.Which term of the AP 2, 6, 10, 14, … is 118? (a) 32nd (b) 31st (c) 29th (d) 30th
  7. 7.What is the 18th term of the AP 13, 15, 17, 19, …? (a) 49 (b) 47 (c) 34 (d) 36
  8. 8.What is the sum of all the whole numbers from 1 to 30? (a) 435 (b) 450 (c) 930 (d) 465
  9. 9.What is the sum of all the whole numbers from 1 to 57? (a) 1596 (b) 1653 (c) 3306 (d) 1654
  10. 10.Which term of the AP 5, 14, 23, 32, … is 329? (a) 36th (b) 39th (c) 37th (d) 38th
  11. 11.What is the sum of the first 25 odd numbers (1 + 3 + 5 + …)? (a) 650 (b) 49 (c) 625 (d) 325
  12. 12.What is the missing term in the AP 1, 9, 17, ?, 33? (a) 24 (b) 25 (c) 33 (d) 26
  13. 13.What is the sum of the first 8 terms of the AP 6, 12, 18, …? (a) 216 (b) 48 (c) 432 (d) 240
  14. 14.What is the 10th term of the AP 12, 14, 16, 18, …? (a) 32 (b) 18 (c) 30 (d) 20
  15. 15.What is the sum of the first 13 odd numbers (1 + 3 + 5 + …)? (a) 91 (b) 25 (c) 182 (d) 169
  16. 16.What is the sum of all the whole numbers from 1 to 99? (a) 4951 (b) 4950 (c) 4851 (d) 9900
  17. 17.What is the missing term in the AP 20, ?, 34, 41, 48? (a) 28 (b) 26 (c) 34 (d) 27
  18. 18.What is the missing term in the AP 1, ?, 7, 10, 13? (a) 3 (b) 7 (c) 4 (d) 5
  19. 19.Which term of the AP 4, 10, 16, 22, … is 64? (a) 13th (b) 12th (c) 11th (d) 10th
  20. 20.What is the 13th term of the AP 10, 18, 26, 34, …? (a) 104 (b) 96 (c) 106 (d) 114
  21. 21.What is the sum of all the whole numbers from 1 to 66? (a) 4422 (b) 2211 (c) 2178 (d) 2145
  22. 22.Which term of the AP 3, 10, 17, 24, … is 136? (a) 20th (b) 19th (c) 21st (d) 22nd
  23. 23.What is the sum of the first 11 odd numbers (1 + 3 + 5 + …)? (a) 121 (b) 21 (c) 66 (d) 132
  24. 24.What is the sum of the first 14 odd numbers (1 + 3 + 5 + …)? (a) 27 (b) 105 (c) 196 (d) 210
  25. 25.What is the sum of the first 5 terms of the AP 8, 9, 10, …? (a) 51 (b) 12 (c) 50 (d) 100
  26. 26.What is the sum of all the whole numbers from 1 to 82? (a) 6806 (b) 3321 (c) 3362 (d) 3403
  27. 27.Which term of the AP 5, 11, 17, 23, … is 221? (a) 38th (b) 39th (c) 37th (d) 36th
  28. 28.What is the missing term in the AP 1, 8, 15, ?, 29? (a) 23 (b) 29 (c) 22 (d) 21
  29. 29.What is the missing term in the AP 9, 18, 27, ?, 45? (a) 45 (b) 36 (c) 37 (d) 35
  30. 30.What is the sum of all the whole numbers from 1 to 41? (a) 820 (b) 862 (c) 1722 (d) 861
  31. 31.What is the 12th term of the AP 4, 7, 10, 13, …? (a) 36 (b) 40 (c) 33 (d) 37
  32. 32.What is the 18th term of the AP 10, 13, 16, 19, …? (a) 54 (b) 61 (c) 51 (d) 64
  33. 33.What is the missing term in the AP 7, 9, 11, ?, 15? (a) 12 (b) 14 (c) 15 (d) 13
  34. 34.What is the sum of the first 10 terms of the AP 3, 7, 11, …? (a) 39 (b) 210 (c) 420 (d) 230
  35. 35.What is the sum of the first 6 terms of the AP 5, 11, 17, …? (a) 120 (b) 138 (c) 35 (d) 240
  36. 36.What is the sum of all the whole numbers from 1 to 17? (a) 306 (b) 153 (c) 154 (d) 136
  37. 37.What is the sum of all the whole numbers from 1 to 20? (a) 420 (b) 190 (c) 210 (d) 200
  38. 38.What is the 29th term of the AP 14, 23, 32, 41, …? (a) 275 (b) 266 (c) 261 (d) 252
  39. 39.What is the sum of the first 23 odd numbers (1 + 3 + 5 + …)? (a) 276 (b) 552 (c) 45 (d) 529
  40. 40.What is the 39th term of the AP 19, 28, 37, 46, …? (a) 361 (b) 342 (c) 370 (d) 351

Answer key

  1. 17
  2. 27
  3. 198
  4. 225
  5. 385
  6. 30th
  7. 47
  8. 465
  9. 1653
  10. 37th
  11. 625
  12. 25
  13. 216
  14. 30
  15. 169
  16. 4950
  17. 27
  18. 4
  19. 11th
  20. 106
  21. 2211
  22. 20th
  23. 121
  24. 196
  25. 50
  26. 3403
  27. 37th
  28. 22
  29. 36
  30. 861
  31. 37
  32. 61
  33. 13
  34. 210
  35. 120
  36. 153
  37. 210
  38. 266
  39. 529
  40. 361

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