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Arithmetic Progression Worksheet for Olympiad

Maths Olympiad topic 29: Sequences and AP · Set 39 · 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 11, 20, 29, ?, 47? (a) 38 (b) 37 (c) 47 (d) 39
  2. 2.What is the missing term in the AP 2, 10, 18, ?, 34? (a) 25 (b) 34 (c) 27 (d) 26
  3. 3.What is the missing term in the AP 8, ?, 16, 20, 24? (a) 12 (b) 11 (c) 13 (d) 16
  4. 4.What is the 17th term of the AP 4, 9, 14, 19, …? (a) 85 (b) 84 (c) 89 (d) 80
  5. 5.What is the 24th term of the AP 6, 12, 18, 24, …? (a) 144 (b) 145 (c) 150 (d) 138
  6. 6.What is the 34th term of the AP 5, 12, 19, 26, …? (a) 243 (b) 238 (c) 231 (d) 236
  7. 7.What is the 19th term of the AP 20, 27, 34, 41, …? (a) 126 (b) 146 (c) 133 (d) 153
  8. 8.What is the missing term in the AP 8, 15, 22, ?, 36? (a) 30 (b) 36 (c) 29 (d) 28
  9. 9.What is the sum of the first 12 terms of the AP 2, 7, 12, …? (a) 384 (b) 57 (c) 354 (d) 708
  10. 10.What is the sum of the first 26 odd numbers (1 + 3 + 5 + …)? (a) 51 (b) 702 (c) 676 (d) 351
  11. 11.What is the sum of the first 5 terms of the AP 1, 2, 3, …? (a) 5 (b) 16 (c) 30 (d) 15
  12. 12.What is the sum of all the whole numbers from 1 to 84? (a) 3528 (b) 3486 (c) 3570 (d) 7140
  13. 13.Which term of the AP 13, 17, 21, 25, … is 73? (a) 15th (b) 17th (c) 18th (d) 16th
  14. 14.Which term of the AP 2, 6, 10, 14, … is 154? (a) 41st (b) 40th (c) 39th (d) 38th
  15. 15.What is the sum of the first 16 odd numbers (1 + 3 + 5 + …)? (a) 272 (b) 31 (c) 256 (d) 136
  16. 16.What is the sum of the first 9 terms of the AP 1, 6, 11, …? (a) 41 (b) 194 (c) 378 (d) 189
  17. 17.What is the 36th term of the AP 4, 10, 16, 22, …? (a) 216 (b) 214 (c) 210 (d) 220
  18. 18.What is the 35th term of the AP 10, 15, 20, 25, …? (a) 180 (b) 170 (c) 185 (d) 175
  19. 19.What is the sum of the first 5 terms of the AP 7, 9, 11, …? (a) 55 (b) 15 (c) 60 (d) 110
  20. 20.What is the 14th term of the AP 8, 12, 16, 20, …? (a) 56 (b) 60 (c) 64 (d) 52
  21. 21.What is the 40th term of the AP 11, 13, 15, 17, …? (a) 91 (b) 80 (c) 89 (d) 78
  22. 22.What is the sum of the first 27 odd numbers (1 + 3 + 5 + …)? (a) 756 (b) 53 (c) 729 (d) 378
  23. 23.What is the sum of the first 11 terms of the AP 9, 13, 17, …? (a) 341 (b) 49 (c) 319 (d) 638
  24. 24.What is the sum of all the whole numbers from 1 to 42? (a) 882 (b) 903 (c) 1806 (d) 861
  25. 25.What is the sum of all the whole numbers from 1 to 36? (a) 1332 (b) 666 (c) 648 (d) 630
  26. 26.What is the 33rd term of the AP 3, 7, 11, 15, …? (a) 132 (b) 131 (c) 128 (d) 135
  27. 27.What is the 33rd term of the AP 19, 21, 23, 25, …? (a) 64 (b) 66 (c) 85 (d) 83
  28. 28.What is the missing term in the AP 12, 19, ?, 33, 40? (a) 33 (b) 27 (c) 25 (d) 26
  29. 29.Which term of the AP 7, 14, 21, 28, … is 210? (a) 30th (b) 29th (c) 31st (d) 32nd
  30. 30.What is the 10th term of the AP 16, 22, 28, 34, …? (a) 60 (b) 76 (c) 70 (d) 54
  31. 31.What is the 25th term of the AP 2, 9, 16, 23, …? (a) 177 (b) 175 (c) 170 (d) 168
  32. 32.What is the sum of all the whole numbers from 1 to 88? (a) 3916 (b) 3828 (c) 3872 (d) 7832
  33. 33.What is the sum of the first 6 terms of the AP 9, 11, 13, …? (a) 19 (b) 168 (c) 90 (d) 84
  34. 34.What is the 26th term of the AP 14, 18, 22, 26, …? (a) 104 (b) 100 (c) 118 (d) 114
  35. 35.What is the sum of the first 10 odd numbers (1 + 3 + 5 + …)? (a) 100 (b) 19 (c) 55 (d) 110
  36. 36.What is the missing term in the AP 14, 18, ?, 26, 30? (a) 21 (b) 22 (c) 23 (d) 26
  37. 37.Which term of the AP 15, 22, 29, 36, … is 148? (a) 19th (b) 21st (c) 22nd (d) 20th
  38. 38.Which term of the AP 2, 4, 6, 8, … is 26? (a) 12th (b) 15th (c) 13th (d) 14th
  39. 39.What is the 26th term of the AP 15, 18, 21, 24, …? (a) 78 (b) 93 (c) 90 (d) 75
  40. 40.What is the sum of the first 11 terms of the AP 6, 7, 8, …? (a) 122 (b) 16 (c) 242 (d) 121

Answer key

  1. 38
  2. 26
  3. 12
  4. 84
  5. 144
  6. 236
  7. 146
  8. 29
  9. 354
  10. 676
  11. 15
  12. 3570
  13. 16th
  14. 39th
  15. 256
  16. 189
  17. 214
  18. 180
  19. 55
  20. 60
  21. 89
  22. 729
  23. 319
  24. 903
  25. 666
  26. 131
  27. 83
  28. 26
  29. 30th
  30. 70
  31. 170
  32. 3916
  33. 84
  34. 114
  35. 100
  36. 22
  37. 20th
  38. 13th
  39. 90
  40. 121

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