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Arithmetic Progression Worksheet for Olympiad

Maths Olympiad topic 29: Sequences and AP · Set 825 · 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 37th term of the AP 19, 26, 33, 40, …? (a) 278 (b) 271 (c) 252 (d) 259
  2. 2.What is the sum of the first 8 odd numbers (1 + 3 + 5 + …)? (a) 72 (b) 64 (c) 36 (d) 15
  3. 3.What is the sum of the first 12 terms of the AP 2, 6, 10, …? (a) 576 (b) 312 (c) 288 (d) 46
  4. 4.What is the sum of all the whole numbers from 1 to 67? (a) 2278 (b) 2211 (c) 4556 (d) 2279
  5. 5.What is the sum of the first 7 terms of the AP 6, 12, 18, …? (a) 336 (b) 42 (c) 168 (d) 189
  6. 6.Which term of the AP 4, 10, 16, 22, … is 94? (a) 15th (b) 18th (c) 17th (d) 16th
  7. 7.What is the sum of the first 6 odd numbers (1 + 3 + 5 + …)? (a) 42 (b) 21 (c) 36 (d) 11
  8. 8.What is the 30th term of the AP 12, 15, 18, 21, …? (a) 99 (b) 90 (c) 102 (d) 87
  9. 9.What is the 38th term of the AP 11, 20, 29, 38, …? (a) 353 (b) 342 (c) 333 (d) 344
  10. 10.Which term of the AP 4, 12, 20, 28, … is 196? (a) 26th (b) 24th (c) 27th (d) 25th
  11. 11.What is the sum of the first 5 terms of the AP 9, 14, 19, …? (a) 29 (b) 100 (c) 190 (d) 95
  12. 12.What is the 32nd term of the AP 12, 14, 16, 18, …? (a) 62 (b) 74 (c) 76 (d) 64
  13. 13.What is the 25th term of the AP 19, 25, 31, 37, …? (a) 169 (b) 144 (c) 150 (d) 163
  14. 14.What is the 33rd term of the AP 18, 24, 30, 36, …? (a) 192 (b) 198 (c) 216 (d) 210
  15. 15.Which term of the AP 12, 19, 26, 33, … is 201? (a) 27th (b) 30th (c) 29th (d) 28th
  16. 16.What is the sum of all the whole numbers from 1 to 17? (a) 136 (b) 306 (c) 154 (d) 153
  17. 17.What is the sum of all the whole numbers from 1 to 47? (a) 1128 (b) 2256 (c) 1129 (d) 1081
  18. 18.What is the missing term in the AP 18, ?, 30, 36, 42? (a) 30 (b) 25 (c) 23 (d) 24
  19. 19.What is the sum of the first 8 terms of the AP 9, 14, 19, …? (a) 212 (b) 44 (c) 424 (d) 232
  20. 20.Which term of the AP 3, 6, 9, 12, … is 66? (a) 22nd (b) 23rd (c) 21st (d) 24th
  21. 21.What is the sum of the first 7 terms of the AP 9, 11, 13, …? (a) 112 (b) 21 (c) 105 (d) 210
  22. 22.What is the 25th term of the AP 14, 22, 30, 38, …? (a) 206 (b) 214 (c) 200 (d) 192
  23. 23.What is the missing term in the AP 12, 14, 16, ?, 20? (a) 17 (b) 20 (c) 19 (d) 18
  24. 24.What is the 34th term of the AP 4, 11, 18, 25, …? (a) 235 (b) 231 (c) 238 (d) 242
  25. 25.What is the sum of the first 11 terms of the AP 1, 3, 5, …? (a) 21 (b) 121 (c) 242 (d) 132
  26. 26.What is the missing term in the AP 8, 14, 20, ?, 32? (a) 25 (b) 27 (c) 26 (d) 32
  27. 27.What is the sum of all the whole numbers from 1 to 11? (a) 132 (b) 67 (c) 66 (d) 55
  28. 28.What is the sum of the first 22 odd numbers (1 + 3 + 5 + …)? (a) 43 (b) 253 (c) 506 (d) 484
  29. 29.What is the 20th term of the AP 14, 17, 20, 23, …? (a) 57 (b) 74 (c) 60 (d) 71
  30. 30.What is the sum of the first 9 terms of the AP 5, 7, 9, …? (a) 234 (b) 21 (c) 117 (d) 126
  31. 31.What is the missing term in the AP 13, 15, ?, 19, 21? (a) 17 (b) 18 (c) 16 (d) 19
  32. 32.What is the 26th term of the AP 8, 16, 24, 32, …? (a) 216 (b) 209 (c) 208 (d) 200
  33. 33.What is the 13th term of the AP 14, 20, 26, 32, …? (a) 72 (b) 92 (c) 86 (d) 78
  34. 34.What is the sum of the first 10 terms of the AP 10, 16, 22, …? (a) 370 (b) 740 (c) 400 (d) 64
  35. 35.What is the 36th term of the AP 7, 12, 17, 22, …? (a) 180 (b) 182 (c) 175 (d) 187
  36. 36.What is the sum of the first 7 terms of the AP 4, 6, 8, …? (a) 77 (b) 70 (c) 16 (d) 140
  37. 37.What is the sum of the first 11 terms of the AP 3, 6, 9, …? (a) 396 (b) 198 (c) 33 (d) 201
  38. 38.What is the missing term in the AP 16, ?, 22, 25, 28? (a) 19 (b) 20 (c) 18 (d) 22
  39. 39.What is the missing term in the AP 6, ?, 10, 12, 14? (a) 9 (b) 7 (c) 10 (d) 8
  40. 40.What is the 20th term of the AP 13, 20, 27, 34, …? (a) 146 (b) 133 (c) 153 (d) 140

Answer key

  1. 271
  2. 64
  3. 288
  4. 2278
  5. 168
  6. 16th
  7. 36
  8. 99
  9. 344
  10. 25th
  11. 95
  12. 74
  13. 163
  14. 210
  15. 28th
  16. 153
  17. 1128
  18. 24
  19. 212
  20. 22nd
  21. 105
  22. 206
  23. 18
  24. 235
  25. 121
  26. 26
  27. 66
  28. 484
  29. 71
  30. 117
  31. 17
  32. 208
  33. 86
  34. 370
  35. 182
  36. 70
  37. 198
  38. 19
  39. 8
  40. 146

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