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Arithmetic Progression Worksheet for Olympiad

Maths Olympiad topic 29: Sequences and AP · Set 309 · 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 sum of the first 10 terms of the AP 7, 8, 9, …? (a) 16 (b) 120 (c) 230 (d) 115
  2. 2.What is the 25th term of the AP 1, 4, 7, 10, …? (a) 72 (b) 76 (c) 73 (d) 75
  3. 3.What is the missing term in the AP 20, 26, ?, 38, 44? (a) 32 (b) 38 (c) 33 (d) 31
  4. 4.What is the missing term in the AP 2, ?, 12, 17, 22? (a) 6 (b) 7 (c) 12 (d) 8
  5. 5.What is the sum of all the whole numbers from 1 to 19? (a) 191 (b) 171 (c) 190 (d) 380
  6. 6.What is the sum of the first 10 terms of the AP 6, 7, 8, …? (a) 110 (b) 210 (c) 105 (d) 15
  7. 7.What is the 35th term of the AP 3, 6, 9, 12, …? (a) 102 (b) 105 (c) 108 (d) 106
  8. 8.What is the missing term in the AP 13, 22, 31, ?, 49? (a) 39 (b) 40 (c) 41 (d) 49
  9. 9.What is the 26th term of the AP 9, 15, 21, 27, …? (a) 156 (b) 150 (c) 159 (d) 165
  10. 10.What is the sum of the first 9 terms of the AP 2, 3, 4, …? (a) 10 (b) 108 (c) 55 (d) 54
  11. 11.What is the 11th term of the AP 2, 8, 14, 20, …? (a) 60 (b) 62 (c) 66 (d) 68
  12. 12.What is the sum of all the whole numbers from 1 to 81? (a) 6642 (b) 3322 (c) 3240 (d) 3321
  13. 13.What is the sum of the first 7 terms of the AP 8, 11, 14, …? (a) 122 (b) 119 (c) 26 (d) 238
  14. 14.What is the 26th term of the AP 5, 12, 19, 26, …? (a) 187 (b) 175 (c) 180 (d) 182
  15. 15.What is the sum of the first 9 terms of the AP 9, 13, 17, …? (a) 41 (b) 450 (c) 243 (d) 225
  16. 16.What is the sum of all the whole numbers from 1 to 76? (a) 2926 (b) 2850 (c) 2888 (d) 5852
  17. 17.What is the 14th term of the AP 17, 24, 31, 38, …? (a) 108 (b) 115 (c) 91 (d) 98
  18. 18.What is the 21st term of the AP 16, 18, 20, 22, …? (a) 40 (b) 42 (c) 58 (d) 56
  19. 19.What is the 11th term of the AP 10, 17, 24, 31, …? (a) 87 (b) 80 (c) 77 (d) 70
  20. 20.What is the sum of the first 10 terms of the AP 1, 7, 13, …? (a) 310 (b) 280 (c) 55 (d) 560
  21. 21.What is the sum of the first 8 odd numbers (1 + 3 + 5 + …)? (a) 36 (b) 15 (c) 64 (d) 72
  22. 22.Which term of the AP 11, 20, 29, 38, … is 200? (a) 22nd (b) 21st (c) 24th (d) 23rd
  23. 23.What is the sum of the first 10 terms of the AP 3, 4, 5, …? (a) 80 (b) 12 (c) 150 (d) 75
  24. 24.What is the sum of the first 16 odd numbers (1 + 3 + 5 + …)? (a) 256 (b) 272 (c) 136 (d) 31
  25. 25.What is the missing term in the AP 11, 18, ?, 32, 39? (a) 26 (b) 24 (c) 25 (d) 32
  26. 26.What is the sum of the first 6 terms of the AP 10, 11, 12, …? (a) 78 (b) 150 (c) 75 (d) 15
  27. 27.Which term of the AP 5, 7, 9, 11, … is 49? (a) 25th (b) 24th (c) 22nd (d) 23rd
  28. 28.What is the 17th term of the AP 12, 19, 26, 33, …? (a) 119 (b) 124 (c) 131 (d) 112
  29. 29.What is the 40th term of the AP 4, 11, 18, 25, …? (a) 277 (b) 273 (c) 284 (d) 280
  30. 30.What is the 17th term of the AP 4, 12, 20, 28, …? (a) 136 (b) 128 (c) 132 (d) 140
  31. 31.What is the 29th term of the AP 20, 27, 34, 41, …? (a) 203 (b) 196 (c) 216 (d) 223
  32. 32.What is the 24th term of the AP 8, 13, 18, 23, …? (a) 120 (b) 128 (c) 115 (d) 123
  33. 33.What is the sum of the first 12 terms of the AP 8, 10, 12, …? (a) 456 (b) 240 (c) 228 (d) 30
  34. 34.What is the sum of the first 9 terms of the AP 9, 14, 19, …? (a) 266 (b) 522 (c) 261 (d) 49
  35. 35.What is the sum of all the whole numbers from 1 to 33? (a) 562 (b) 561 (c) 1122 (d) 528
  36. 36.Which term of the AP 7, 9, 11, 13, … is 55? (a) 26th (b) 24th (c) 27th (d) 25th
  37. 37.What is the sum of all the whole numbers from 1 to 99? (a) 4950 (b) 4851 (c) 9900 (d) 4951
  38. 38.What is the missing term in the AP 2, ?, 8, 11, 14? (a) 8 (b) 5 (c) 6 (d) 4
  39. 39.What is the sum of the first 7 terms of the AP 1, 5, 9, …? (a) 182 (b) 105 (c) 25 (d) 91
  40. 40.Which term of the AP 9, 13, 17, 21, … is 73? (a) 16th (b) 18th (c) 19th (d) 17th

Answer key

  1. 115
  2. 73
  3. 32
  4. 7
  5. 190
  6. 105
  7. 105
  8. 40
  9. 159
  10. 54
  11. 62
  12. 3321
  13. 119
  14. 180
  15. 225
  16. 2926
  17. 108
  18. 56
  19. 80
  20. 280
  21. 64
  22. 22nd
  23. 75
  24. 256
  25. 25
  26. 75
  27. 23rd
  28. 124
  29. 277
  30. 132
  31. 216
  32. 123
  33. 228
  34. 261
  35. 561
  36. 25th
  37. 4950
  38. 5
  39. 91
  40. 17th

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