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Arithmetic Progression Worksheet for Olympiad

Maths Olympiad topic 29: Sequences and AP · Set 414 · 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 38th term of the AP 12, 17, 22, 27, …? (a) 190 (b) 185 (c) 197 (d) 202
  2. 2.What is the sum of the first 7 terms of the AP 8, 11, 14, …? (a) 122 (b) 26 (c) 119 (d) 238
  3. 3.What is the 35th term of the AP 16, 24, 32, 40, …? (a) 272 (b) 280 (c) 288 (d) 296
  4. 4.What is the 15th term of the AP 6, 11, 16, 21, …? (a) 81 (b) 70 (c) 76 (d) 75
  5. 5.What is the 22nd term of the AP 1, 9, 17, 25, …? (a) 168 (b) 169 (c) 176 (d) 177
  6. 6.What is the missing term in the AP 18, 22, ?, 30, 34? (a) 25 (b) 27 (c) 26 (d) 30
  7. 7.What is the 33rd term of the AP 2, 9, 16, 23, …? (a) 233 (b) 226 (c) 224 (d) 231
  8. 8.What is the sum of the first 5 terms of the AP 6, 9, 12, …? (a) 60 (b) 18 (c) 63 (d) 120
  9. 9.What is the 36th term of the AP 10, 16, 22, 28, …? (a) 220 (b) 226 (c) 210 (d) 216
  10. 10.What is the sum of all the whole numbers from 1 to 41? (a) 820 (b) 861 (c) 1722 (d) 862
  11. 11.Which term of the AP 19, 28, 37, 46, … is 262? (a) 30th (b) 29th (c) 27th (d) 28th
  12. 12.What is the 12th term of the AP 14, 21, 28, 35, …? (a) 98 (b) 84 (c) 91 (d) 77
  13. 13.What is the 16th term of the AP 18, 21, 24, 27, …? (a) 48 (b) 66 (c) 63 (d) 45
  14. 14.What is the sum of the first 30 odd numbers (1 + 3 + 5 + …)? (a) 900 (b) 465 (c) 930 (d) 59
  15. 15.What is the sum of the first 18 odd numbers (1 + 3 + 5 + …)? (a) 342 (b) 171 (c) 324 (d) 35
  16. 16.What is the sum of the first 7 terms of the AP 8, 10, 12, …? (a) 20 (b) 98 (c) 105 (d) 196
  17. 17.What is the 12th term of the AP 19, 23, 27, 31, …? (a) 48 (b) 44 (c) 63 (d) 67
  18. 18.Which term of the AP 20, 28, 36, 44, … is 84? (a) 9th (b) 11th (c) 8th (d) 10th
  19. 19.What is the 27th term of the AP 16, 18, 20, 22, …? (a) 54 (b) 68 (c) 52 (d) 70
  20. 20.What is the missing term in the AP 18, ?, 32, 39, 46? (a) 24 (b) 25 (c) 26 (d) 32
  21. 21.What is the sum of the first 28 odd numbers (1 + 3 + 5 + …)? (a) 812 (b) 55 (c) 406 (d) 784
  22. 22.What is the 12th term of the AP 2, 11, 20, 29, …? (a) 99 (b) 108 (c) 101 (d) 110
  23. 23.What is the sum of all the whole numbers from 1 to 37? (a) 704 (b) 666 (c) 1406 (d) 703
  24. 24.What is the sum of the first 11 terms of the AP 9, 11, 13, …? (a) 418 (b) 29 (c) 209 (d) 220
  25. 25.What is the missing term in the AP 2, 7, 12, ?, 22? (a) 16 (b) 17 (c) 22 (d) 18
  26. 26.What is the 40th term of the AP 5, 10, 15, 20, …? (a) 201 (b) 205 (c) 200 (d) 195
  27. 27.What is the sum of the first 6 terms of the AP 3, 8, 13, …? (a) 186 (b) 93 (c) 28 (d) 108
  28. 28.What is the missing term in the AP 13, ?, 19, 22, 25? (a) 19 (b) 15 (c) 16 (d) 17
  29. 29.What is the sum of the first 5 odd numbers (1 + 3 + 5 + …)? (a) 9 (b) 30 (c) 15 (d) 25
  30. 30.What is the sum of all the whole numbers from 1 to 19? (a) 380 (b) 171 (c) 190 (d) 191
  31. 31.What is the missing term in the AP 9, ?, 19, 24, 29? (a) 13 (b) 14 (c) 19 (d) 15
  32. 32.What is the sum of all the whole numbers from 1 to 29? (a) 436 (b) 870 (c) 435 (d) 406
  33. 33.What is the sum of the first 8 odd numbers (1 + 3 + 5 + …)? (a) 64 (b) 15 (c) 72 (d) 36
  34. 34.What is the 25th term of the AP 2, 5, 8, 11, …? (a) 72 (b) 74 (c) 77 (d) 75
  35. 35.What is the sum of the first 6 terms of the AP 9, 11, 13, …? (a) 90 (b) 19 (c) 84 (d) 168
  36. 36.What is the 14th term of the AP 1, 6, 11, 16, …? (a) 65 (b) 71 (c) 70 (d) 66
  37. 37.What is the 24th term of the AP 2, 6, 10, 14, …? (a) 98 (b) 96 (c) 94 (d) 92
  38. 38.What is the sum of the first 8 terms of the AP 8, 14, 20, …? (a) 464 (b) 256 (c) 50 (d) 232
  39. 39.Which term of the AP 3, 10, 17, 24, … is 94? (a) 13th (b) 15th (c) 16th (d) 14th
  40. 40.What is the sum of the first 10 terms of the AP 6, 8, 10, …? (a) 24 (b) 160 (c) 150 (d) 300

Answer key

  1. 197
  2. 119
  3. 288
  4. 76
  5. 169
  6. 26
  7. 226
  8. 60
  9. 220
  10. 861
  11. 28th
  12. 91
  13. 63
  14. 900
  15. 324
  16. 98
  17. 63
  18. 9th
  19. 68
  20. 25
  21. 784
  22. 101
  23. 703
  24. 209
  25. 17
  26. 200
  27. 93
  28. 16
  29. 25
  30. 190
  31. 14
  32. 435
  33. 64
  34. 74
  35. 84
  36. 66
  37. 94
  38. 232
  39. 14th
  40. 150

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