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Arithmetic Progression Worksheet for Olympiad

Maths Olympiad topic 29: Sequences and AP · Set 276 · 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 15, ?, 27, 33, 39? (a) 22 (b) 21 (c) 27 (d) 20
  2. 2.What is the sum of the first 6 terms of the AP 6, 8, 10, …? (a) 16 (b) 132 (c) 66 (d) 72
  3. 3.What is the sum of all the whole numbers from 1 to 74? (a) 2775 (b) 2738 (c) 2701 (d) 5550
  4. 4.What is the 19th term of the AP 6, 11, 16, 21, …? (a) 101 (b) 95 (c) 96 (d) 90
  5. 5.What is the 28th term of the AP 5, 8, 11, 14, …? (a) 81 (b) 84 (c) 89 (d) 86
  6. 6.What is the sum of all the whole numbers from 1 to 99? (a) 4951 (b) 4950 (c) 9900 (d) 4851
  7. 7.What is the sum of the first 8 odd numbers (1 + 3 + 5 + …)? (a) 64 (b) 72 (c) 36 (d) 15
  8. 8.What is the sum of the first 7 terms of the AP 5, 11, 17, …? (a) 182 (b) 161 (c) 41 (d) 322
  9. 9.Which term of the AP 15, 23, 31, 39, … is 159? (a) 21st (b) 18th (c) 20th (d) 19th
  10. 10.What is the 37th term of the AP 17, 19, 21, 23, …? (a) 91 (b) 74 (c) 72 (d) 89
  11. 11.What is the 36th term of the AP 17, 23, 29, 35, …? (a) 227 (b) 233 (c) 210 (d) 216
  12. 12.What is the sum of the first 12 terms of the AP 7, 12, 17, …? (a) 828 (b) 444 (c) 414 (d) 62
  13. 13.What is the sum of the first 8 terms of the AP 3, 7, 11, …? (a) 272 (b) 152 (c) 31 (d) 136
  14. 14.Which term of the AP 11, 17, 23, 29, … is 131? (a) 20th (b) 21st (c) 22nd (d) 23rd
  15. 15.What is the 28th term of the AP 9, 17, 25, 33, …? (a) 224 (b) 233 (c) 216 (d) 225
  16. 16.What is the missing term in the AP 16, ?, 28, 34, 40? (a) 23 (b) 22 (c) 28 (d) 21
  17. 17.What is the sum of the first 12 terms of the AP 5, 10, 15, …? (a) 780 (b) 60 (c) 420 (d) 390
  18. 18.What is the missing term in the AP 18, 26, ?, 42, 50? (a) 42 (b) 34 (c) 33 (d) 35
  19. 19.What is the sum of the first 7 terms of the AP 6, 10, 14, …? (a) 140 (b) 126 (c) 252 (d) 30
  20. 20.Which term of the AP 1, 4, 7, 10, … is 97? (a) 34th (b) 35th (c) 32nd (d) 33rd
  21. 21.What is the 26th term of the AP 2, 8, 14, 20, …? (a) 150 (b) 158 (c) 156 (d) 152
  22. 22.What is the missing term in the AP 20, ?, 28, 32, 36? (a) 23 (b) 24 (c) 25 (d) 28
  23. 23.What is the 17th term of the AP 1, 10, 19, 28, …? (a) 153 (b) 144 (c) 145 (d) 154
  24. 24.What is the sum of all the whole numbers from 1 to 96? (a) 4608 (b) 4560 (c) 9312 (d) 4656
  25. 25.What is the sum of the first 11 terms of the AP 3, 8, 13, …? (a) 308 (b) 53 (c) 616 (d) 313
  26. 26.Which term of the AP 7, 13, 19, 25, … is 79? (a) 12th (b) 14th (c) 15th (d) 13th
  27. 27.What is the 29th term of the AP 7, 13, 19, 25, …? (a) 174 (b) 175 (c) 181 (d) 168
  28. 28.What is the sum of the first 7 odd numbers (1 + 3 + 5 + …)? (a) 56 (b) 49 (c) 13 (d) 28
  29. 29.What is the sum of all the whole numbers from 1 to 87? (a) 3741 (b) 3829 (c) 7656 (d) 3828
  30. 30.What is the sum of the first 11 terms of the AP 3, 6, 9, …? (a) 198 (b) 396 (c) 201 (d) 33
  31. 31.What is the missing term in the AP 4, ?, 18, 25, 32? (a) 18 (b) 11 (c) 10 (d) 12
  32. 32.What is the sum of the first 5 odd numbers (1 + 3 + 5 + …)? (a) 30 (b) 9 (c) 25 (d) 15
  33. 33.What is the 14th term of the AP 2, 11, 20, 29, …? (a) 128 (b) 126 (c) 117 (d) 119
  34. 34.What is the missing term in the AP 14, 22, 30, ?, 46? (a) 38 (b) 46 (c) 39 (d) 37
  35. 35.What is the 31st term of the AP 13, 20, 27, 34, …? (a) 223 (b) 230 (c) 210 (d) 217
  36. 36.What is the 18th term of the AP 10, 15, 20, 25, …? (a) 90 (b) 85 (c) 100 (d) 95
  37. 37.What is the sum of all the whole numbers from 1 to 12? (a) 66 (b) 72 (c) 78 (d) 156
  38. 38.What is the sum of the first 12 terms of the AP 3, 5, 7, …? (a) 336 (b) 25 (c) 180 (d) 168
  39. 39.What is the sum of the first 11 terms of the AP 4, 10, 16, …? (a) 748 (b) 64 (c) 407 (d) 374
  40. 40.What is the 19th term of the AP 19, 23, 27, 31, …? (a) 76 (b) 95 (c) 72 (d) 91

Answer key

  1. 21
  2. 66
  3. 2775
  4. 96
  5. 86
  6. 4950
  7. 64
  8. 161
  9. 19th
  10. 89
  11. 227
  12. 414
  13. 136
  14. 21st
  15. 225
  16. 22
  17. 390
  18. 34
  19. 126
  20. 33rd
  21. 152
  22. 24
  23. 145
  24. 4656
  25. 308
  26. 13th
  27. 175
  28. 49
  29. 3828
  30. 198
  31. 11
  32. 25
  33. 119
  34. 38
  35. 223
  36. 95
  37. 78
  38. 168
  39. 374
  40. 91

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