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Arithmetic Progression Worksheet for Olympiad

Maths Olympiad topic 29: Sequences and AP · Set 541 · 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 26th term of the AP 7, 13, 19, 25, …? (a) 156 (b) 150 (c) 163 (d) 157
  2. 2.Which term of the AP 11, 13, 15, 17, … is 77? (a) 36th (b) 35th (c) 34th (d) 33rd
  3. 3.What is the missing term in the AP 19, 25, ?, 37, 43? (a) 37 (b) 31 (c) 32 (d) 30
  4. 4.What is the 18th term of the AP 18, 20, 22, 24, …? (a) 36 (b) 54 (c) 34 (d) 52
  5. 5.What is the 28th term of the AP 4, 10, 16, 22, …? (a) 172 (b) 166 (c) 162 (d) 168
  6. 6.What is the sum of the first 5 terms of the AP 3, 5, 7, …? (a) 70 (b) 40 (c) 35 (d) 11
  7. 7.What is the sum of the first 5 terms of the AP 9, 14, 19, …? (a) 29 (b) 95 (c) 190 (d) 100
  8. 8.What is the sum of the first 8 terms of the AP 2, 8, 14, …? (a) 44 (b) 368 (c) 184 (d) 208
  9. 9.Which term of the AP 11, 18, 25, 32, … is 137? (a) 21st (b) 20th (c) 19th (d) 18th
  10. 10.What is the sum of the first 8 terms of the AP 9, 12, 15, …? (a) 30 (b) 168 (c) 156 (d) 312
  11. 11.What is the 32nd term of the AP 9, 18, 27, 36, …? (a) 288 (b) 289 (c) 279 (d) 297
  12. 12.What is the sum of the first 15 odd numbers (1 + 3 + 5 + …)? (a) 29 (b) 240 (c) 225 (d) 120
  13. 13.What is the sum of the first 26 odd numbers (1 + 3 + 5 + …)? (a) 351 (b) 51 (c) 676 (d) 702
  14. 14.Which term of the AP 1, 9, 17, 25, … is 225? (a) 29th (b) 31st (c) 30th (d) 28th
  15. 15.What is the sum of all the whole numbers from 1 to 76? (a) 5852 (b) 2888 (c) 2926 (d) 2850
  16. 16.What is the sum of the first 10 odd numbers (1 + 3 + 5 + …)? (a) 100 (b) 110 (c) 19 (d) 55
  17. 17.What is the sum of all the whole numbers from 1 to 32? (a) 1056 (b) 512 (c) 528 (d) 496
  18. 18.What is the 20th term of the AP 1, 3, 5, 7, …? (a) 39 (b) 40 (c) 41 (d) 38
  19. 19.What is the 40th term of the AP 1, 5, 9, 13, …? (a) 161 (b) 160 (c) 157 (d) 156
  20. 20.What is the 39th term of the AP 14, 23, 32, 41, …? (a) 351 (b) 365 (c) 342 (d) 356
  21. 21.What is the sum of the first 12 terms of the AP 7, 12, 17, …? (a) 828 (b) 444 (c) 414 (d) 62
  22. 22.What is the sum of the first 9 terms of the AP 6, 8, 10, …? (a) 22 (b) 135 (c) 126 (d) 252
  23. 23.What is the sum of the first 6 terms of the AP 8, 9, 10, …? (a) 63 (b) 126 (c) 66 (d) 13
  24. 24.Which term of the AP 17, 25, 33, 41, … is 305? (a) 39th (b) 36th (c) 38th (d) 37th
  25. 25.What is the sum of all the whole numbers from 1 to 25? (a) 325 (b) 300 (c) 650 (d) 326
  26. 26.What is the missing term in the AP 20, 22, 24, ?, 28? (a) 25 (b) 28 (c) 26 (d) 27
  27. 27.What is the sum of the first 9 terms of the AP 1, 5, 9, …? (a) 171 (b) 153 (c) 306 (d) 33
  28. 28.What is the sum of the first 9 terms of the AP 7, 10, 13, …? (a) 31 (b) 171 (c) 174 (d) 342
  29. 29.What is the 19th term of the AP 1, 5, 9, 13, …? (a) 77 (b) 76 (c) 72 (d) 73
  30. 30.What is the 26th term of the AP 10, 19, 28, 37, …? (a) 234 (b) 235 (c) 244 (d) 225
  31. 31.What is the sum of the first 8 terms of the AP 7, 10, 13, …? (a) 152 (b) 280 (c) 140 (d) 28
  32. 32.What is the missing term in the AP 1, 4, ?, 10, 13? (a) 10 (b) 8 (c) 6 (d) 7
  33. 33.What is the 15th term of the AP 17, 22, 27, 32, …? (a) 87 (b) 70 (c) 75 (d) 92
  34. 34.What is the 11th term of the AP 10, 17, 24, 31, …? (a) 80 (b) 77 (c) 70 (d) 87
  35. 35.What is the sum of all the whole numbers from 1 to 67? (a) 2211 (b) 4556 (c) 2278 (d) 2279
  36. 36.What is the 27th term of the AP 7, 9, 11, 13, …? (a) 54 (b) 52 (c) 59 (d) 61
  37. 37.What is the sum of all the whole numbers from 1 to 37? (a) 704 (b) 1406 (c) 666 (d) 703
  38. 38.What is the missing term in the AP 11, ?, 15, 17, 19? (a) 15 (b) 12 (c) 14 (d) 13
  39. 39.What is the 38th term of the AP 19, 21, 23, 25, …? (a) 76 (b) 93 (c) 95 (d) 74
  40. 40.Which term of the AP 10, 14, 18, 22, … is 146? (a) 34th (b) 37th (c) 35th (d) 36th

Answer key

  1. 157
  2. 34th
  3. 31
  4. 52
  5. 166
  6. 35
  7. 95
  8. 184
  9. 19th
  10. 156
  11. 288
  12. 225
  13. 676
  14. 29th
  15. 2926
  16. 100
  17. 528
  18. 39
  19. 157
  20. 356
  21. 414
  22. 126
  23. 63
  24. 37th
  25. 325
  26. 26
  27. 153
  28. 171
  29. 73
  30. 235
  31. 140
  32. 7
  33. 87
  34. 80
  35. 2278
  36. 59
  37. 703
  38. 13
  39. 93
  40. 35th

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