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Arithmetic Progression Worksheet for Olympiad

Maths Olympiad topic 29: Sequences and AP · Set 193 · 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 39th term of the AP 16, 18, 20, 22, …? (a) 76 (b) 92 (c) 94 (d) 78
  2. 2.What is the sum of the first 11 terms of the AP 1, 3, 5, …? (a) 132 (b) 242 (c) 21 (d) 121
  3. 3.What is the 40th term of the AP 6, 14, 22, 30, …? (a) 318 (b) 326 (c) 312 (d) 320
  4. 4.What is the 19th term of the AP 11, 20, 29, 38, …? (a) 182 (b) 173 (c) 171 (d) 162
  5. 5.What is the missing term in the AP 14, 22, ?, 38, 46? (a) 31 (b) 38 (c) 29 (d) 30
  6. 6.What is the missing term in the AP 18, ?, 36, 45, 54? (a) 36 (b) 26 (c) 27 (d) 28
  7. 7.Which term of the AP 16, 25, 34, 43, … is 322? (a) 35th (b) 36th (c) 37th (d) 34th
  8. 8.What is the 17th term of the AP 11, 15, 19, 23, …? (a) 79 (b) 64 (c) 75 (d) 68
  9. 9.What is the sum of the first 23 odd numbers (1 + 3 + 5 + …)? (a) 276 (b) 45 (c) 552 (d) 529
  10. 10.Which term of the AP 4, 10, 16, 22, … is 190? (a) 34th (b) 33rd (c) 32nd (d) 31st
  11. 11.What is the sum of all the whole numbers from 1 to 33? (a) 528 (b) 562 (c) 1122 (d) 561
  12. 12.Which term of the AP 1, 5, 9, 13, … is 85? (a) 24th (b) 22nd (c) 23rd (d) 21st
  13. 13.What is the 10th term of the AP 3, 6, 9, 12, …? (a) 27 (b) 31 (c) 33 (d) 30
  14. 14.What is the missing term in the AP 2, 11, ?, 29, 38? (a) 19 (b) 29 (c) 20 (d) 21
  15. 15.What is the sum of all the whole numbers from 1 to 66? (a) 2178 (b) 2145 (c) 2211 (d) 4422
  16. 16.What is the sum of all the whole numbers from 1 to 45? (a) 2070 (b) 1035 (c) 1036 (d) 990
  17. 17.What is the 14th term of the AP 10, 17, 24, 31, …? (a) 108 (b) 98 (c) 91 (d) 101
  18. 18.What is the sum of the first 8 terms of the AP 10, 11, 12, …? (a) 17 (b) 112 (c) 216 (d) 108
  19. 19.What is the sum of the first 8 terms of the AP 1, 7, 13, …? (a) 200 (b) 43 (c) 352 (d) 176
  20. 20.Which term of the AP 4, 10, 16, 22, … is 196? (a) 33rd (b) 32nd (c) 35th (d) 34th
  21. 21.What is the sum of the first 11 odd numbers (1 + 3 + 5 + …)? (a) 66 (b) 132 (c) 121 (d) 21
  22. 22.What is the missing term in the AP 7, 11, ?, 19, 23? (a) 16 (b) 19 (c) 15 (d) 14
  23. 23.What is the 28th term of the AP 12, 18, 24, 30, …? (a) 162 (b) 168 (c) 180 (d) 174
  24. 24.What is the sum of the first 9 odd numbers (1 + 3 + 5 + …)? (a) 45 (b) 90 (c) 81 (d) 17
  25. 25.What is the sum of all the whole numbers from 1 to 80? (a) 3240 (b) 3160 (c) 6480 (d) 3200
  26. 26.What is the sum of the first 9 terms of the AP 10, 13, 16, …? (a) 198 (b) 201 (c) 34 (d) 396
  27. 27.What is the 35th term of the AP 3, 9, 15, 21, …? (a) 207 (b) 213 (c) 210 (d) 204
  28. 28.Which term of the AP 20, 26, 32, 38, … is 146? (a) 22nd (b) 23rd (c) 21st (d) 24th
  29. 29.What is the sum of the first 9 terms of the AP 10, 14, 18, …? (a) 252 (b) 42 (c) 234 (d) 468
  30. 30.What is the missing term in the AP 18, 22, 26, ?, 34? (a) 30 (b) 29 (c) 34 (d) 31
  31. 31.What is the missing term in the AP 16, 19, 22, ?, 28? (a) 26 (b) 25 (c) 28 (d) 24
  32. 32.What is the 39th term of the AP 17, 25, 33, 41, …? (a) 312 (b) 329 (c) 304 (d) 321
  33. 33.What is the sum of all the whole numbers from 1 to 21? (a) 232 (b) 210 (c) 462 (d) 231
  34. 34.What is the 13th term of the AP 8, 11, 14, 17, …? (a) 44 (b) 47 (c) 39 (d) 36
  35. 35.What is the missing term in the AP 20, 24, 28, ?, 36? (a) 36 (b) 32 (c) 31 (d) 33
  36. 36.What is the sum of the first 7 terms of the AP 7, 8, 9, …? (a) 71 (b) 140 (c) 70 (d) 13
  37. 37.What is the sum of the first 21 odd numbers (1 + 3 + 5 + …)? (a) 231 (b) 462 (c) 441 (d) 41
  38. 38.What is the 10th term of the AP 18, 22, 26, 30, …? (a) 40 (b) 54 (c) 36 (d) 58
  39. 39.What is the 12th term of the AP 20, 23, 26, 29, …? (a) 36 (b) 56 (c) 33 (d) 53
  40. 40.What is the missing term in the AP 15, ?, 31, 39, 47? (a) 22 (b) 31 (c) 24 (d) 23

Answer key

  1. 92
  2. 121
  3. 318
  4. 173
  5. 30
  6. 27
  7. 35th
  8. 75
  9. 529
  10. 32nd
  11. 561
  12. 22nd
  13. 30
  14. 20
  15. 2211
  16. 1035
  17. 101
  18. 108
  19. 176
  20. 33rd
  21. 121
  22. 15
  23. 174
  24. 81
  25. 3240
  26. 198
  27. 207
  28. 22nd
  29. 234
  30. 30
  31. 25
  32. 321
  33. 231
  34. 44
  35. 32
  36. 70
  37. 441
  38. 54
  39. 53
  40. 23

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