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Arithmetic Progression Worksheet for Olympiad

Maths Olympiad topic 29: Sequences and AP · Set 542 · 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 15th term of the AP 9, 17, 25, 33, …? (a) 112 (b) 129 (c) 121 (d) 120
  2. 2.What is the 16th term of the AP 10, 12, 14, 16, …? (a) 32 (b) 40 (c) 30 (d) 42
  3. 3.What is the sum of the first 8 terms of the AP 9, 13, 17, …? (a) 200 (b) 37 (c) 184 (d) 368
  4. 4.What is the missing term in the AP 10, ?, 16, 19, 22? (a) 14 (b) 16 (c) 12 (d) 13
  5. 5.What is the 10th term of the AP 16, 22, 28, 34, …? (a) 60 (b) 54 (c) 76 (d) 70
  6. 6.What is the sum of the first 11 terms of the AP 4, 5, 6, …? (a) 14 (b) 100 (c) 198 (d) 99
  7. 7.What is the sum of the first 6 terms of the AP 9, 11, 13, …? (a) 168 (b) 84 (c) 19 (d) 90
  8. 8.What is the missing term in the AP 13, ?, 27, 34, 41? (a) 21 (b) 19 (c) 27 (d) 20
  9. 9.What is the sum of the first 29 odd numbers (1 + 3 + 5 + …)? (a) 870 (b) 841 (c) 57 (d) 435
  10. 10.What is the sum of the first 12 terms of the AP 1, 6, 11, …? (a) 56 (b) 684 (c) 372 (d) 342
  11. 11.What is the 33rd term of the AP 15, 22, 29, 36, …? (a) 231 (b) 224 (c) 239 (d) 246
  12. 12.What is the missing term in the AP 18, 26, ?, 42, 50? (a) 34 (b) 35 (c) 42 (d) 33
  13. 13.What is the 13th term of the AP 6, 12, 18, 24, …? (a) 79 (b) 78 (c) 72 (d) 84
  14. 14.Which term of the AP 10, 17, 24, 31, … is 73? (a) 12th (b) 9th (c) 11th (d) 10th
  15. 15.What is the sum of the first 5 terms of the AP 9, 11, 13, …? (a) 65 (b) 130 (c) 17 (d) 70
  16. 16.Which term of the AP 6, 15, 24, 33, … is 78? (a) 9th (b) 10th (c) 8th (d) 11th
  17. 17.What is the sum of all the whole numbers from 1 to 93? (a) 4371 (b) 8742 (c) 4278 (d) 4372
  18. 18.What is the sum of the first 14 odd numbers (1 + 3 + 5 + …)? (a) 196 (b) 210 (c) 27 (d) 105
  19. 19.What is the 39th term of the AP 4, 12, 20, 28, …? (a) 304 (b) 316 (c) 312 (d) 308
  20. 20.What is the sum of the first 9 terms of the AP 10, 12, 14, …? (a) 26 (b) 324 (c) 162 (d) 171
  21. 21.What is the 22nd term of the AP 10, 17, 24, 31, …? (a) 157 (b) 164 (c) 154 (d) 147
  22. 22.What is the 34th term of the AP 18, 25, 32, 39, …? (a) 231 (b) 249 (c) 238 (d) 256
  23. 23.What is the sum of all the whole numbers from 1 to 33? (a) 561 (b) 1122 (c) 528 (d) 562
  24. 24.What is the 40th term of the AP 17, 23, 29, 35, …? (a) 234 (b) 240 (c) 257 (d) 251
  25. 25.What is the 20th term of the AP 13, 19, 25, 31, …? (a) 114 (b) 127 (c) 133 (d) 120
  26. 26.What is the sum of the first 28 odd numbers (1 + 3 + 5 + …)? (a) 812 (b) 406 (c) 55 (d) 784
  27. 27.What is the sum of all the whole numbers from 1 to 34? (a) 561 (b) 1190 (c) 595 (d) 578
  28. 28.What is the 13th term of the AP 20, 23, 26, 29, …? (a) 59 (b) 36 (c) 56 (d) 39
  29. 29.What is the sum of all the whole numbers from 1 to 86? (a) 3741 (b) 3698 (c) 3655 (d) 7482
  30. 30.What is the sum of the first 11 terms of the AP 6, 10, 14, …? (a) 308 (b) 572 (c) 286 (d) 46
  31. 31.Which term of the AP 8, 14, 20, 26, … is 170? (a) 27th (b) 30th (c) 28th (d) 29th
  32. 32.What is the sum of all the whole numbers from 1 to 64? (a) 2016 (b) 4160 (c) 2048 (d) 2080
  33. 33.What is the sum of the first 23 odd numbers (1 + 3 + 5 + …)? (a) 552 (b) 45 (c) 529 (d) 276
  34. 34.What is the sum of the first 19 odd numbers (1 + 3 + 5 + …)? (a) 190 (b) 37 (c) 361 (d) 380
  35. 35.What is the 28th term of the AP 10, 16, 22, 28, …? (a) 178 (b) 168 (c) 162 (d) 172
  36. 36.What is the 12th term of the AP 4, 11, 18, 25, …? (a) 77 (b) 81 (c) 84 (d) 88
  37. 37.Which term of the AP 1, 10, 19, 28, … is 127? (a) 17th (b) 16th (c) 15th (d) 14th
  38. 38.Which term of the AP 4, 6, 8, 10, … is 60? (a) 28th (b) 31st (c) 30th (d) 29th
  39. 39.Which term of the AP 17, 25, 33, 41, … is 105? (a) 11th (b) 14th (c) 13th (d) 12th
  40. 40.What is the sum of the first 6 terms of the AP 10, 11, 12, …? (a) 15 (b) 78 (c) 150 (d) 75

Answer key

  1. 121
  2. 40
  3. 184
  4. 13
  5. 70
  6. 99
  7. 84
  8. 20
  9. 841
  10. 342
  11. 239
  12. 34
  13. 78
  14. 10th
  15. 65
  16. 9th
  17. 4371
  18. 196
  19. 308
  20. 162
  21. 157
  22. 249
  23. 561
  24. 251
  25. 127
  26. 784
  27. 595
  28. 56
  29. 3741
  30. 286
  31. 28th
  32. 2080
  33. 529
  34. 361
  35. 172
  36. 81
  37. 15th
  38. 29th
  39. 12th
  40. 75

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