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Arithmetic Progression Worksheet for Olympiad

Maths Olympiad topic 29: Sequences and AP · Set 453 · 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 24th term of the AP 10, 14, 18, 22, …? (a) 92 (b) 102 (c) 96 (d) 106
  2. 2.What is the 26th term of the AP 5, 9, 13, 17, …? (a) 100 (b) 105 (c) 104 (d) 109
  3. 3.What is the sum of the first 10 terms of the AP 10, 16, 22, …? (a) 370 (b) 400 (c) 64 (d) 740
  4. 4.Which term of the AP 7, 14, 21, 28, … is 77? (a) 10th (b) 13th (c) 12th (d) 11th
  5. 5.What is the sum of the first 9 terms of the AP 5, 11, 17, …? (a) 288 (b) 522 (c) 261 (d) 53
  6. 6.What is the 22nd term of the AP 7, 11, 15, 19, …? (a) 91 (b) 95 (c) 88 (d) 84
  7. 7.What is the missing term in the AP 16, 18, ?, 22, 24? (a) 21 (b) 22 (c) 20 (d) 19
  8. 8.What is the 16th term of the AP 9, 17, 25, 33, …? (a) 128 (b) 129 (c) 137 (d) 120
  9. 9.Which term of the AP 20, 22, 24, 26, … is 66? (a) 24th (b) 25th (c) 23rd (d) 33rd
  10. 10.What is the sum of the first 23 odd numbers (1 + 3 + 5 + …)? (a) 529 (b) 45 (c) 276 (d) 552
  11. 11.What is the sum of all the whole numbers from 1 to 93? (a) 4278 (b) 4372 (c) 8742 (d) 4371
  12. 12.What is the sum of all the whole numbers from 1 to 14? (a) 98 (b) 91 (c) 105 (d) 210
  13. 13.What is the sum of all the whole numbers from 1 to 42? (a) 861 (b) 903 (c) 882 (d) 1806
  14. 14.What is the missing term in the AP 12, 21, 30, ?, 48? (a) 48 (b) 39 (c) 38 (d) 40
  15. 15.What is the sum of all the whole numbers from 1 to 100? (a) 4950 (b) 5050 (c) 5000 (d) 10100
  16. 16.Which term of the AP 10, 14, 18, 22, … is 50? (a) 12th (b) 13th (c) 10th (d) 11th
  17. 17.What is the 24th term of the AP 5, 8, 11, 14, …? (a) 77 (b) 69 (c) 72 (d) 74
  18. 18.What is the missing term in the AP 15, 18, 21, ?, 27? (a) 25 (b) 23 (c) 24 (d) 27
  19. 19.What is the sum of all the whole numbers from 1 to 90? (a) 4095 (b) 8190 (c) 4005 (d) 4050
  20. 20.What is the missing term in the AP 4, ?, 18, 25, 32? (a) 12 (b) 10 (c) 18 (d) 11
  21. 21.What is the sum of the first 9 terms of the AP 5, 6, 7, …? (a) 82 (b) 81 (c) 13 (d) 162
  22. 22.What is the 38th term of the AP 7, 15, 23, 31, …? (a) 296 (b) 303 (c) 304 (d) 311
  23. 23.What is the sum of the first 15 odd numbers (1 + 3 + 5 + …)? (a) 120 (b) 225 (c) 240 (d) 29
  24. 24.What is the sum of the first 8 terms of the AP 6, 10, 14, …? (a) 176 (b) 320 (c) 34 (d) 160
  25. 25.What is the sum of the first 7 terms of the AP 6, 9, 12, …? (a) 108 (b) 210 (c) 24 (d) 105
  26. 26.What is the 22nd term of the AP 19, 25, 31, 37, …? (a) 126 (b) 151 (c) 145 (d) 132
  27. 27.What is the sum of the first 8 terms of the AP 7, 11, 15, …? (a) 184 (b) 168 (c) 336 (d) 35
  28. 28.What is the 11th term of the AP 16, 20, 24, 28, …? (a) 44 (b) 60 (c) 56 (d) 40
  29. 29.What is the sum of all the whole numbers from 1 to 82? (a) 3403 (b) 6806 (c) 3321 (d) 3362
  30. 30.What is the sum of the first 12 terms of the AP 6, 10, 14, …? (a) 672 (b) 336 (c) 50 (d) 360
  31. 31.What is the 29th term of the AP 2, 7, 12, 17, …? (a) 140 (b) 142 (c) 145 (d) 147
  32. 32.What is the missing term in the AP 7, 14, ?, 28, 35? (a) 20 (b) 21 (c) 22 (d) 28
  33. 33.What is the missing term in the AP 2, ?, 20, 29, 38? (a) 20 (b) 10 (c) 11 (d) 12
  34. 34.What is the 40th term of the AP 19, 25, 31, 37, …? (a) 253 (b) 259 (c) 234 (d) 240
  35. 35.What is the sum of the first 9 terms of the AP 4, 7, 10, …? (a) 144 (b) 288 (c) 147 (d) 28
  36. 36.What is the missing term in the AP 18, 27, ?, 45, 54? (a) 35 (b) 37 (c) 45 (d) 36
  37. 37.What is the sum of the first 12 terms of the AP 5, 8, 11, …? (a) 516 (b) 38 (c) 258 (d) 276
  38. 38.What is the missing term in the AP 18, 25, ?, 39, 46? (a) 39 (b) 32 (c) 33 (d) 31
  39. 39.What is the sum of the first 7 terms of the AP 8, 13, 18, …? (a) 166 (b) 322 (c) 38 (d) 161
  40. 40.What is the sum of the first 7 terms of the AP 3, 8, 13, …? (a) 252 (b) 33 (c) 126 (d) 131

Answer key

  1. 102
  2. 105
  3. 370
  4. 11th
  5. 261
  6. 91
  7. 20
  8. 129
  9. 24th
  10. 529
  11. 4371
  12. 105
  13. 903
  14. 39
  15. 5050
  16. 11th
  17. 74
  18. 24
  19. 4095
  20. 11
  21. 81
  22. 303
  23. 225
  24. 160
  25. 105
  26. 145
  27. 168
  28. 56
  29. 3403
  30. 336
  31. 142
  32. 21
  33. 11
  34. 253
  35. 144
  36. 36
  37. 258
  38. 32
  39. 161
  40. 126

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