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Arithmetic Progression Worksheet for Olympiad

Maths Olympiad topic 29: Sequences and AP · Set 167 · 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 3, 12, 21, ?, 39? (a) 31 (b) 30 (c) 29 (d) 39
  2. 2.What is the sum of the first 5 terms of the AP 4, 10, 16, …? (a) 28 (b) 160 (c) 95 (d) 80
  3. 3.What is the 30th term of the AP 11, 14, 17, 20, …? (a) 101 (b) 98 (c) 90 (d) 87
  4. 4.What is the sum of all the whole numbers from 1 to 47? (a) 1129 (b) 1128 (c) 2256 (d) 1081
  5. 5.What is the sum of the first 25 odd numbers (1 + 3 + 5 + …)? (a) 625 (b) 49 (c) 325 (d) 650
  6. 6.What is the sum of the first 10 terms of the AP 2, 8, 14, …? (a) 290 (b) 56 (c) 320 (d) 580
  7. 7.What is the missing term in the AP 16, 19, ?, 25, 28? (a) 22 (b) 25 (c) 23 (d) 21
  8. 8.What is the 21st term of the AP 8, 11, 14, 17, …? (a) 71 (b) 68 (c) 60 (d) 63
  9. 9.Which term of the AP 14, 22, 30, 38, … is 286? (a) 36th (b) 35th (c) 37th (d) 34th
  10. 10.What is the 36th term of the AP 13, 19, 25, 31, …? (a) 216 (b) 223 (c) 210 (d) 229
  11. 11.What is the sum of the first 5 terms of the AP 8, 12, 16, …? (a) 80 (b) 160 (c) 24 (d) 90
  12. 12.What is the sum of all the whole numbers from 1 to 70? (a) 2450 (b) 4970 (c) 2485 (d) 2415
  13. 13.What is the sum of all the whole numbers from 1 to 27? (a) 756 (b) 379 (c) 351 (d) 378
  14. 14.Which term of the AP 16, 19, 22, 25, … is 58? (a) 14th (b) 17th (c) 16th (d) 15th
  15. 15.What is the sum of the first 6 terms of the AP 3, 8, 13, …? (a) 28 (b) 186 (c) 93 (d) 108
  16. 16.What is the sum of the first 8 odd numbers (1 + 3 + 5 + …)? (a) 72 (b) 64 (c) 36 (d) 15
  17. 17.What is the sum of all the whole numbers from 1 to 14? (a) 210 (b) 105 (c) 91 (d) 98
  18. 18.What is the sum of the first 8 terms of the AP 4, 7, 10, …? (a) 232 (b) 128 (c) 116 (d) 25
  19. 19.What is the sum of the first 14 odd numbers (1 + 3 + 5 + …)? (a) 105 (b) 210 (c) 27 (d) 196
  20. 20.What is the 33rd term of the AP 9, 17, 25, 33, …? (a) 256 (b) 264 (c) 265 (d) 273
  21. 21.What is the sum of the first 9 terms of the AP 3, 5, 7, …? (a) 198 (b) 19 (c) 99 (d) 108
  22. 22.What is the missing term in the AP 19, ?, 27, 31, 35? (a) 27 (b) 22 (c) 24 (d) 23
  23. 23.What is the sum of the first 10 odd numbers (1 + 3 + 5 + …)? (a) 100 (b) 19 (c) 110 (d) 55
  24. 24.What is the sum of all the whole numbers from 1 to 85? (a) 3570 (b) 3655 (c) 7310 (d) 3656
  25. 25.What is the 35th term of the AP 4, 12, 20, 28, …? (a) 276 (b) 272 (c) 284 (d) 280
  26. 26.What is the missing term in the AP 3, 7, ?, 15, 19? (a) 10 (b) 12 (c) 15 (d) 11
  27. 27.What is the 13th term of the AP 1, 6, 11, 16, …? (a) 66 (b) 61 (c) 65 (d) 60
  28. 28.What is the sum of all the whole numbers from 1 to 75? (a) 2850 (b) 2775 (c) 2851 (d) 5700
  29. 29.What is the sum of the first 6 terms of the AP 6, 10, 14, …? (a) 108 (b) 96 (c) 192 (d) 26
  30. 30.What is the sum of the first 15 odd numbers (1 + 3 + 5 + …)? (a) 29 (b) 120 (c) 240 (d) 225
  31. 31.What is the 15th term of the AP 16, 18, 20, 22, …? (a) 44 (b) 30 (c) 46 (d) 28
  32. 32.What is the 22nd term of the AP 11, 18, 25, 32, …? (a) 154 (b) 147 (c) 165 (d) 158
  33. 33.Which term of the AP 3, 12, 21, 30, … is 219? (a) 25th (b) 26th (c) 24th (d) 27th
  34. 34.What is the 32nd term of the AP 16, 23, 30, 37, …? (a) 224 (b) 233 (c) 217 (d) 240
  35. 35.What is the 37th term of the AP 3, 12, 21, 30, …? (a) 336 (b) 327 (c) 333 (d) 324
  36. 36.What is the missing term in the AP 9, 16, ?, 30, 37? (a) 23 (b) 24 (c) 22 (d) 30
  37. 37.Which term of the AP 4, 6, 8, 10, … is 30? (a) 15th (b) 13th (c) 16th (d) 14th
  38. 38.What is the 31st term of the AP 20, 27, 34, 41, …? (a) 237 (b) 210 (c) 230 (d) 217
  39. 39.What is the sum of the first 5 terms of the AP 8, 14, 20, …? (a) 100 (b) 200 (c) 32 (d) 115
  40. 40.What is the sum of the first 10 terms of the AP 6, 12, 18, …? (a) 60 (b) 360 (c) 660 (d) 330

Answer key

  1. 30
  2. 80
  3. 98
  4. 1128
  5. 625
  6. 290
  7. 22
  8. 68
  9. 35th
  10. 223
  11. 80
  12. 2485
  13. 378
  14. 15th
  15. 93
  16. 64
  17. 105
  18. 116
  19. 196
  20. 265
  21. 99
  22. 23
  23. 100
  24. 3655
  25. 276
  26. 11
  27. 61
  28. 2850
  29. 96
  30. 225
  31. 44
  32. 158
  33. 25th
  34. 233
  35. 327
  36. 23
  37. 14th
  38. 230
  39. 100
  40. 330

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