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Arithmetic Progression Worksheet for Olympiad

Maths Olympiad topic 29: Sequences and AP · Set 500 · 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 30th term of the AP 18, 26, 34, 42, …? (a) 250 (b) 232 (c) 258 (d) 240
  2. 2.What is the 27th term of the AP 18, 27, 36, 45, …? (a) 243 (b) 261 (c) 234 (d) 252
  3. 3.What is the sum of the first 10 terms of the AP 3, 5, 7, …? (a) 240 (b) 130 (c) 120 (d) 21
  4. 4.What is the 35th term of the AP 16, 25, 34, 43, …? (a) 322 (b) 306 (c) 315 (d) 331
  5. 5.What is the sum of the first 6 odd numbers (1 + 3 + 5 + …)? (a) 11 (b) 42 (c) 36 (d) 21
  6. 6.What is the sum of the first 5 terms of the AP 10, 12, 14, …? (a) 18 (b) 70 (c) 75 (d) 140
  7. 7.What is the 30th term of the AP 3, 7, 11, 15, …? (a) 120 (b) 123 (c) 119 (d) 116
  8. 8.Which term of the AP 3, 6, 9, 12, … is 102? (a) 36th (b) 33rd (c) 34th (d) 35th
  9. 9.What is the 12th term of the AP 5, 7, 9, 11, …? (a) 24 (b) 22 (c) 27 (d) 29
  10. 10.Which term of the AP 9, 13, 17, 21, … is 133? (a) 31st (b) 33rd (c) 32nd (d) 34th
  11. 11.Which term of the AP 1, 3, 5, 7, … is 19? (a) 12th (b) 9th (c) 10th (d) 11th
  12. 12.What is the sum of the first 16 odd numbers (1 + 3 + 5 + …)? (a) 31 (b) 136 (c) 272 (d) 256
  13. 13.What is the 15th term of the AP 12, 19, 26, 33, …? (a) 117 (b) 105 (c) 110 (d) 98
  14. 14.What is the 39th term of the AP 4, 12, 20, 28, …? (a) 316 (b) 312 (c) 304 (d) 308
  15. 15.What is the missing term in the AP 15, 24, 33, ?, 51? (a) 51 (b) 42 (c) 43 (d) 41
  16. 16.What is the 35th term of the AP 7, 14, 21, 28, …? (a) 245 (b) 252 (c) 246 (d) 238
  17. 17.Which term of the AP 10, 19, 28, 37, … is 262? (a) 28th (b) 30th (c) 31st (d) 29th
  18. 18.What is the 34th term of the AP 11, 19, 27, 35, …? (a) 275 (b) 272 (c) 283 (d) 264
  19. 19.What is the 36th term of the AP 17, 20, 23, 26, …? (a) 108 (b) 122 (c) 105 (d) 125
  20. 20.What is the sum of the first 12 terms of the AP 9, 10, 11, …? (a) 20 (b) 348 (c) 174 (d) 180
  21. 21.What is the 11th term of the AP 16, 20, 24, 28, …? (a) 56 (b) 44 (c) 60 (d) 40
  22. 22.What is the sum of all the whole numbers from 1 to 82? (a) 3362 (b) 6806 (c) 3321 (d) 3403
  23. 23.Which term of the AP 14, 22, 30, 38, … is 86? (a) 11th (b) 12th (c) 9th (d) 10th
  24. 24.What is the 30th term of the AP 16, 24, 32, 40, …? (a) 232 (b) 256 (c) 248 (d) 240
  25. 25.What is the missing term in the AP 2, 4, 6, ?, 10? (a) 9 (b) 10 (c) 7 (d) 8
  26. 26.What is the sum of the first 8 terms of the AP 4, 9, 14, …? (a) 192 (b) 39 (c) 344 (d) 172
  27. 27.What is the missing term in the AP 20, 26, 32, ?, 44? (a) 37 (b) 39 (c) 38 (d) 44
  28. 28.What is the 16th term of the AP 10, 16, 22, 28, …? (a) 90 (b) 96 (c) 100 (d) 106
  29. 29.What is the 40th term of the AP 2, 7, 12, 17, …? (a) 200 (b) 195 (c) 197 (d) 202
  30. 30.What is the sum of all the whole numbers from 1 to 52? (a) 1378 (b) 2756 (c) 1352 (d) 1326
  31. 31.What is the sum of the first 6 terms of the AP 8, 10, 12, …? (a) 78 (b) 18 (c) 156 (d) 84
  32. 32.What is the sum of the first 6 terms of the AP 9, 13, 17, …? (a) 228 (b) 29 (c) 114 (d) 126
  33. 33.What is the 31st term of the AP 13, 15, 17, 19, …? (a) 73 (b) 62 (c) 75 (d) 60
  34. 34.What is the sum of all the whole numbers from 1 to 36? (a) 666 (b) 648 (c) 630 (d) 1332
  35. 35.What is the 19th term of the AP 13, 16, 19, 22, …? (a) 70 (b) 57 (c) 54 (d) 67
  36. 36.What is the 26th term of the AP 11, 19, 27, 35, …? (a) 219 (b) 208 (c) 211 (d) 200
  37. 37.What is the sum of the first 10 terms of the AP 2, 4, 6, …? (a) 120 (b) 220 (c) 110 (d) 20
  38. 38.What is the sum of the first 12 odd numbers (1 + 3 + 5 + …)? (a) 23 (b) 156 (c) 144 (d) 78
  39. 39.What is the 35th term of the AP 17, 26, 35, 44, …? (a) 332 (b) 323 (c) 306 (d) 315
  40. 40.What is the sum of the first 17 odd numbers (1 + 3 + 5 + …)? (a) 153 (b) 289 (c) 33 (d) 306

Answer key

  1. 250
  2. 252
  3. 120
  4. 322
  5. 36
  6. 70
  7. 119
  8. 34th
  9. 27
  10. 32nd
  11. 10th
  12. 256
  13. 110
  14. 308
  15. 42
  16. 245
  17. 29th
  18. 275
  19. 122
  20. 174
  21. 56
  22. 3403
  23. 10th
  24. 248
  25. 8
  26. 172
  27. 38
  28. 100
  29. 197
  30. 1378
  31. 78
  32. 114
  33. 73
  34. 666
  35. 67
  36. 211
  37. 110
  38. 144
  39. 323
  40. 289

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