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Arithmetic Progression Worksheet for Olympiad

Maths Olympiad topic 29: Sequences and AP · Set 511 · 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 5, 7, ?, 11, 13? (a) 8 (b) 9 (c) 10 (d) 11
  2. 2.What is the missing term in the AP 3, 6, ?, 12, 15? (a) 9 (b) 8 (c) 10 (d) 12
  3. 3.What is the sum of the first 5 terms of the AP 10, 16, 22, …? (a) 110 (b) 125 (c) 220 (d) 34
  4. 4.What is the sum of the first 7 terms of the AP 5, 9, 13, …? (a) 29 (b) 133 (c) 238 (d) 119
  5. 5.What is the sum of the first 22 odd numbers (1 + 3 + 5 + …)? (a) 253 (b) 506 (c) 484 (d) 43
  6. 6.Which term of the AP 14, 20, 26, 32, … is 212? (a) 35th (b) 36th (c) 34th (d) 33rd
  7. 7.What is the 38th term of the AP 16, 18, 20, 22, …? (a) 74 (b) 90 (c) 92 (d) 76
  8. 8.What is the sum of the first 8 terms of the AP 2, 3, 4, …? (a) 44 (b) 48 (c) 88 (d) 9
  9. 9.What is the missing term in the AP 1, 8, ?, 22, 29? (a) 15 (b) 22 (c) 14 (d) 16
  10. 10.What is the sum of the first 5 terms of the AP 1, 2, 3, …? (a) 30 (b) 16 (c) 5 (d) 15
  11. 11.What is the sum of all the whole numbers from 1 to 88? (a) 3872 (b) 7832 (c) 3916 (d) 3828
  12. 12.What is the sum of the first 14 odd numbers (1 + 3 + 5 + …)? (a) 27 (b) 105 (c) 196 (d) 210
  13. 13.What is the sum of all the whole numbers from 1 to 76? (a) 2888 (b) 2926 (c) 5852 (d) 2850
  14. 14.What is the 35th term of the AP 12, 19, 26, 33, …? (a) 245 (b) 257 (c) 238 (d) 250
  15. 15.What is the 20th term of the AP 6, 12, 18, 24, …? (a) 120 (b) 126 (c) 114 (d) 121
  16. 16.What is the sum of the first 5 terms of the AP 8, 14, 20, …? (a) 200 (b) 32 (c) 100 (d) 115
  17. 17.What is the missing term in the AP 1, 7, 13, ?, 25? (a) 19 (b) 25 (c) 20 (d) 18
  18. 18.What is the missing term in the AP 6, 12, 18, ?, 30? (a) 25 (b) 23 (c) 24 (d) 30
  19. 19.What is the sum of the first 6 terms of the AP 3, 4, 5, …? (a) 66 (b) 33 (c) 8 (d) 36
  20. 20.What is the sum of the first 12 terms of the AP 1, 3, 5, …? (a) 156 (b) 144 (c) 288 (d) 23
  21. 21.What is the sum of all the whole numbers from 1 to 52? (a) 1352 (b) 1378 (c) 2756 (d) 1326
  22. 22.What is the sum of the first 18 odd numbers (1 + 3 + 5 + …)? (a) 171 (b) 324 (c) 342 (d) 35
  23. 23.What is the missing term in the AP 10, ?, 24, 31, 38? (a) 18 (b) 16 (c) 24 (d) 17
  24. 24.What is the 13th term of the AP 2, 6, 10, 14, …? (a) 52 (b) 50 (c) 48 (d) 54
  25. 25.What is the 29th term of the AP 19, 25, 31, 37, …? (a) 174 (b) 187 (c) 168 (d) 193
  26. 26.What is the sum of all the whole numbers from 1 to 32? (a) 512 (b) 496 (c) 1056 (d) 528
  27. 27.What is the 37th term of the AP 10, 16, 22, 28, …? (a) 216 (b) 222 (c) 226 (d) 232
  28. 28.Which term of the AP 16, 18, 20, 22, … is 48? (a) 18th (b) 24th (c) 16th (d) 17th
  29. 29.What is the 25th term of the AP 14, 20, 26, 32, …? (a) 150 (b) 144 (c) 158 (d) 164
  30. 30.What is the sum of the first 10 terms of the AP 5, 10, 15, …? (a) 50 (b) 275 (c) 550 (d) 300
  31. 31.What is the sum of the first 9 terms of the AP 1, 7, 13, …? (a) 225 (b) 49 (c) 252 (d) 450
  32. 32.What is the sum of the first 16 odd numbers (1 + 3 + 5 + …)? (a) 31 (b) 256 (c) 136 (d) 272
  33. 33.What is the sum of the first 13 odd numbers (1 + 3 + 5 + …)? (a) 91 (b) 182 (c) 25 (d) 169
  34. 34.What is the 40th term of the AP 1, 7, 13, 19, …? (a) 234 (b) 235 (c) 240 (d) 241
  35. 35.What is the sum of the first 6 terms of the AP 3, 8, 13, …? (a) 108 (b) 28 (c) 186 (d) 93
  36. 36.What is the 34th term of the AP 13, 19, 25, 31, …? (a) 198 (b) 217 (c) 204 (d) 211
  37. 37.What is the sum of all the whole numbers from 1 to 33? (a) 562 (b) 561 (c) 528 (d) 1122
  38. 38.What is the sum of the first 8 terms of the AP 5, 8, 11, …? (a) 124 (b) 26 (c) 248 (d) 136
  39. 39.What is the sum of all the whole numbers from 1 to 80? (a) 6480 (b) 3160 (c) 3200 (d) 3240
  40. 40.What is the sum of the first 7 terms of the AP 5, 7, 9, …? (a) 77 (b) 154 (c) 17 (d) 84

Answer key

  1. 9
  2. 9
  3. 110
  4. 119
  5. 484
  6. 34th
  7. 90
  8. 44
  9. 15
  10. 15
  11. 3916
  12. 196
  13. 2926
  14. 250
  15. 120
  16. 100
  17. 19
  18. 24
  19. 33
  20. 144
  21. 1378
  22. 324
  23. 17
  24. 50
  25. 187
  26. 528
  27. 226
  28. 17th
  29. 158
  30. 275
  31. 225
  32. 256
  33. 169
  34. 235
  35. 93
  36. 211
  37. 561
  38. 124
  39. 3240
  40. 77

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