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Arithmetic Progression Worksheet for Olympiad

Maths Olympiad topic 29: Sequences and AP · Set 465 · 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 12, ?, 30, 39, 48? (a) 22 (b) 30 (c) 21 (d) 20
  2. 2.What is the sum of the first 9 terms of the AP 6, 7, 8, …? (a) 91 (b) 90 (c) 14 (d) 180
  3. 3.What is the sum of the first 8 terms of the AP 9, 10, 11, …? (a) 200 (b) 16 (c) 100 (d) 104
  4. 4.Which term of the AP 4, 13, 22, 31, … is 139? (a) 17th (b) 15th (c) 16th (d) 18th
  5. 5.What is the 22nd term of the AP 17, 21, 25, 29, …? (a) 88 (b) 84 (c) 105 (d) 101
  6. 6.What is the sum of the first 21 odd numbers (1 + 3 + 5 + …)? (a) 41 (b) 231 (c) 462 (d) 441
  7. 7.What is the sum of all the whole numbers from 1 to 65? (a) 2145 (b) 2080 (c) 4290 (d) 2146
  8. 8.Which term of the AP 13, 18, 23, 28, … is 158? (a) 32nd (b) 30th (c) 31st (d) 29th
  9. 9.What is the sum of all the whole numbers from 1 to 26? (a) 351 (b) 702 (c) 338 (d) 325
  10. 10.What is the sum of the first 16 odd numbers (1 + 3 + 5 + …)? (a) 31 (b) 256 (c) 272 (d) 136
  11. 11.What is the missing term in the AP 4, ?, 18, 25, 32? (a) 10 (b) 11 (c) 12 (d) 18
  12. 12.What is the sum of the first 6 terms of the AP 5, 9, 13, …? (a) 180 (b) 90 (c) 102 (d) 25
  13. 13.Which term of the AP 9, 18, 27, 36, … is 333? (a) 39th (b) 38th (c) 36th (d) 37th
  14. 14.What is the sum of the first 7 terms of the AP 4, 8, 12, …? (a) 112 (b) 224 (c) 28 (d) 126
  15. 15.What is the sum of all the whole numbers from 1 to 68? (a) 2346 (b) 2312 (c) 2278 (d) 4692
  16. 16.What is the 13th term of the AP 7, 9, 11, 13, …? (a) 31 (b) 33 (c) 26 (d) 24
  17. 17.What is the missing term in the AP 17, ?, 25, 29, 33? (a) 21 (b) 25 (c) 22 (d) 20
  18. 18.What is the sum of the first 10 terms of the AP 9, 13, 17, …? (a) 45 (b) 540 (c) 270 (d) 290
  19. 19.Which term of the AP 7, 10, 13, 16, … is 97? (a) 33rd (b) 30th (c) 31st (d) 32nd
  20. 20.What is the sum of the first 28 odd numbers (1 + 3 + 5 + …)? (a) 812 (b) 406 (c) 784 (d) 55
  21. 21.What is the sum of all the whole numbers from 1 to 69? (a) 4830 (b) 2346 (c) 2415 (d) 2416
  22. 22.What is the 14th term of the AP 9, 12, 15, 18, …? (a) 42 (b) 48 (c) 39 (d) 51
  23. 23.Which term of the AP 2, 4, 6, 8, … is 48? (a) 23rd (b) 26th (c) 24th (d) 25th
  24. 24.Which term of the AP 2, 8, 14, 20, … is 122? (a) 20th (b) 23rd (c) 21st (d) 22nd
  25. 25.What is the sum of the first 9 terms of the AP 2, 6, 10, …? (a) 180 (b) 34 (c) 162 (d) 324
  26. 26.What is the sum of the first 27 odd numbers (1 + 3 + 5 + …)? (a) 729 (b) 53 (c) 378 (d) 756
  27. 27.What is the sum of all the whole numbers from 1 to 17? (a) 154 (b) 153 (c) 136 (d) 306
  28. 28.What is the sum of all the whole numbers from 1 to 24? (a) 600 (b) 300 (c) 276 (d) 288
  29. 29.Which term of the AP 4, 11, 18, 25, … is 172? (a) 27th (b) 26th (c) 25th (d) 24th
  30. 30.What is the sum of the first 10 terms of the AP 10, 12, 14, …? (a) 190 (b) 200 (c) 380 (d) 28
  31. 31.What is the 30th term of the AP 19, 23, 27, 31, …? (a) 139 (b) 120 (c) 116 (d) 135
  32. 32.What is the sum of the first 8 terms of the AP 6, 11, 16, …? (a) 376 (b) 208 (c) 41 (d) 188
  33. 33.What is the missing term in the AP 5, 8, ?, 14, 17? (a) 11 (b) 14 (c) 12 (d) 10
  34. 34.What is the missing term in the AP 1, ?, 11, 16, 21? (a) 5 (b) 6 (c) 11 (d) 7
  35. 35.What is the sum of the first 7 terms of the AP 4, 6, 8, …? (a) 70 (b) 140 (c) 77 (d) 16
  36. 36.What is the sum of the first 12 terms of the AP 9, 14, 19, …? (a) 64 (b) 438 (c) 468 (d) 876
  37. 37.What is the 15th term of the AP 19, 21, 23, 25, …? (a) 30 (b) 49 (c) 47 (d) 28
  38. 38.What is the 32nd term of the AP 10, 18, 26, 34, …? (a) 266 (b) 258 (c) 256 (d) 248
  39. 39.What is the sum of all the whole numbers from 1 to 33? (a) 561 (b) 528 (c) 562 (d) 1122
  40. 40.Which term of the AP 16, 23, 30, 37, … is 121? (a) 17th (b) 15th (c) 16th (d) 18th

Answer key

  1. 21
  2. 90
  3. 100
  4. 16th
  5. 101
  6. 441
  7. 2145
  8. 30th
  9. 351
  10. 256
  11. 11
  12. 90
  13. 37th
  14. 112
  15. 2346
  16. 31
  17. 21
  18. 270
  19. 31st
  20. 784
  21. 2415
  22. 48
  23. 24th
  24. 21st
  25. 162
  26. 729
  27. 153
  28. 300
  29. 25th
  30. 190
  31. 135
  32. 188
  33. 11
  34. 6
  35. 70
  36. 438
  37. 47
  38. 258
  39. 561
  40. 16th

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