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Arithmetic Progression Worksheet for Olympiad

Maths Olympiad topic 29: Sequences and AP · Set 479 · 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 5 terms of the AP 9, 10, 11, …? (a) 56 (b) 110 (c) 55 (d) 13
  2. 2.Which term of the AP 3, 12, 21, 30, … is 201? (a) 23rd (b) 22nd (c) 25th (d) 24th
  3. 3.What is the sum of all the whole numbers from 1 to 20? (a) 200 (b) 210 (c) 190 (d) 420
  4. 4.What is the 15th term of the AP 8, 16, 24, 32, …? (a) 112 (b) 128 (c) 121 (d) 120
  5. 5.What is the 33rd term of the AP 10, 19, 28, 37, …? (a) 307 (b) 298 (c) 297 (d) 288
  6. 6.Which term of the AP 8, 15, 22, 29, … is 162? (a) 25th (b) 22nd (c) 24th (d) 23rd
  7. 7.What is the missing term in the AP 14, 21, 28, ?, 42? (a) 36 (b) 42 (c) 34 (d) 35
  8. 8.What is the 30th term of the AP 9, 11, 13, 15, …? (a) 60 (b) 58 (c) 67 (d) 69
  9. 9.What is the sum of all the whole numbers from 1 to 49? (a) 1225 (b) 1176 (c) 2450 (d) 1226
  10. 10.What is the 17th term of the AP 16, 23, 30, 37, …? (a) 135 (b) 128 (c) 119 (d) 112
  11. 11.What is the missing term in the AP 3, 9, ?, 21, 27? (a) 16 (b) 15 (c) 21 (d) 14
  12. 12.What is the 29th term of the AP 18, 20, 22, 24, …? (a) 58 (b) 76 (c) 74 (d) 56
  13. 13.What is the sum of the first 7 terms of the AP 9, 13, 17, …? (a) 147 (b) 294 (c) 33 (d) 161
  14. 14.What is the sum of the first 6 terms of the AP 1, 5, 9, …? (a) 66 (b) 21 (c) 132 (d) 78
  15. 15.What is the sum of the first 10 odd numbers (1 + 3 + 5 + …)? (a) 55 (b) 100 (c) 110 (d) 19
  16. 16.What is the sum of the first 9 terms of the AP 8, 13, 18, …? (a) 504 (b) 257 (c) 252 (d) 48
  17. 17.What is the missing term in the AP 12, ?, 24, 30, 36? (a) 24 (b) 19 (c) 17 (d) 18
  18. 18.What is the sum of the first 16 odd numbers (1 + 3 + 5 + …)? (a) 136 (b) 31 (c) 272 (d) 256
  19. 19.What is the sum of the first 19 odd numbers (1 + 3 + 5 + …)? (a) 380 (b) 361 (c) 190 (d) 37
  20. 20.What is the sum of the first 7 odd numbers (1 + 3 + 5 + …)? (a) 13 (b) 28 (c) 49 (d) 56
  21. 21.Which term of the AP 3, 5, 7, 9, … is 47? (a) 25th (b) 22nd (c) 24th (d) 23rd
  22. 22.What is the sum of all the whole numbers from 1 to 73? (a) 2628 (b) 2701 (c) 2702 (d) 5402
  23. 23.What is the sum of the first 9 terms of the AP 1, 7, 13, …? (a) 450 (b) 49 (c) 225 (d) 252
  24. 24.What is the missing term in the AP 4, ?, 14, 19, 24? (a) 8 (b) 10 (c) 9 (d) 14
  25. 25.What is the 35th term of the AP 16, 22, 28, 34, …? (a) 226 (b) 204 (c) 210 (d) 220
  26. 26.What is the 29th term of the AP 2, 6, 10, 14, …? (a) 114 (b) 112 (c) 116 (d) 118
  27. 27.What is the sum of the first 5 terms of the AP 10, 12, 14, …? (a) 140 (b) 75 (c) 70 (d) 18
  28. 28.What is the sum of the first 15 odd numbers (1 + 3 + 5 + …)? (a) 240 (b) 29 (c) 120 (d) 225
  29. 29.What is the sum of the first 12 odd numbers (1 + 3 + 5 + …)? (a) 23 (b) 156 (c) 144 (d) 78
  30. 30.What is the sum of the first 7 terms of the AP 8, 14, 20, …? (a) 203 (b) 44 (c) 182 (d) 364
  31. 31.What is the sum of the first 7 terms of the AP 10, 12, 14, …? (a) 119 (b) 224 (c) 112 (d) 22
  32. 32.What is the sum of the first 6 terms of the AP 1, 2, 3, …? (a) 42 (b) 24 (c) 21 (d) 6
  33. 33.What is the 40th term of the AP 4, 11, 18, 25, …? (a) 280 (b) 284 (c) 277 (d) 273
  34. 34.Which term of the AP 14, 23, 32, 41, … is 95? (a) 11th (b) 9th (c) 12th (d) 10th
  35. 35.What is the sum of the first 5 terms of the AP 4, 6, 8, …? (a) 40 (b) 45 (c) 12 (d) 80
  36. 36.What is the missing term in the AP 16, ?, 30, 37, 44? (a) 24 (b) 22 (c) 23 (d) 30
  37. 37.What is the missing term in the AP 7, 11, ?, 19, 23? (a) 16 (b) 14 (c) 19 (d) 15
  38. 38.What is the sum of the first 12 terms of the AP 4, 10, 16, …? (a) 888 (b) 70 (c) 480 (d) 444
  39. 39.What is the sum of all the whole numbers from 1 to 100? (a) 5050 (b) 10100 (c) 5000 (d) 4950
  40. 40.What is the sum of all the whole numbers from 1 to 21? (a) 232 (b) 231 (c) 210 (d) 462

Answer key

  1. 55
  2. 23rd
  3. 210
  4. 120
  5. 298
  6. 23rd
  7. 35
  8. 67
  9. 1225
  10. 128
  11. 15
  12. 74
  13. 147
  14. 66
  15. 100
  16. 252
  17. 18
  18. 256
  19. 361
  20. 49
  21. 23rd
  22. 2701
  23. 225
  24. 9
  25. 220
  26. 114
  27. 70
  28. 225
  29. 144
  30. 182
  31. 112
  32. 21
  33. 277
  34. 10th
  35. 40
  36. 23
  37. 15
  38. 444
  39. 5050
  40. 231

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