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Arithmetic Progression Worksheet for Olympiad

Maths Olympiad topic 29: Sequences and AP · Set 953 · 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 1, ?, 5, 7, 9? (a) 5 (b) 4 (c) 3 (d) 2
  2. 2.What is the 16th term of the AP 5, 12, 19, 26, …? (a) 110 (b) 105 (c) 112 (d) 117
  3. 3.What is the 37th term of the AP 14, 16, 18, 20, …? (a) 72 (b) 74 (c) 86 (d) 88
  4. 4.Which term of the AP 6, 12, 18, 24, … is 120? (a) 19th (b) 21st (c) 22nd (d) 20th
  5. 5.What is the 27th term of the AP 15, 23, 31, 39, …? (a) 231 (b) 208 (c) 216 (d) 223
  6. 6.What is the sum of all the whole numbers from 1 to 59? (a) 1771 (b) 1770 (c) 3540 (d) 1711
  7. 7.Which term of the AP 3, 12, 21, 30, … is 129? (a) 15th (b) 17th (c) 14th (d) 16th
  8. 8.What is the 15th term of the AP 17, 24, 31, 38, …? (a) 98 (b) 122 (c) 115 (d) 105
  9. 9.What is the sum of the first 25 odd numbers (1 + 3 + 5 + …)? (a) 650 (b) 49 (c) 325 (d) 625
  10. 10.What is the 34th term of the AP 1, 3, 5, 7, …? (a) 68 (b) 66 (c) 67 (d) 69
  11. 11.What is the sum of the first 19 odd numbers (1 + 3 + 5 + …)? (a) 380 (b) 361 (c) 37 (d) 190
  12. 12.What is the sum of the first 6 terms of the AP 6, 10, 14, …? (a) 96 (b) 192 (c) 26 (d) 108
  13. 13.What is the 22nd term of the AP 8, 16, 24, 32, …? (a) 184 (b) 177 (c) 168 (d) 176
  14. 14.What is the sum of the first 11 odd numbers (1 + 3 + 5 + …)? (a) 132 (b) 121 (c) 66 (d) 21
  15. 15.What is the sum of the first 20 odd numbers (1 + 3 + 5 + …)? (a) 39 (b) 420 (c) 400 (d) 210
  16. 16.What is the sum of the first 8 terms of the AP 3, 9, 15, …? (a) 45 (b) 192 (c) 216 (d) 384
  17. 17.What is the 16th term of the AP 2, 11, 20, 29, …? (a) 137 (b) 144 (c) 135 (d) 146
  18. 18.What is the missing term in the AP 13, 18, 23, ?, 33? (a) 29 (b) 33 (c) 28 (d) 27
  19. 19.What is the sum of the first 5 terms of the AP 6, 12, 18, …? (a) 30 (b) 90 (c) 105 (d) 180
  20. 20.What is the missing term in the AP 18, ?, 28, 33, 38? (a) 22 (b) 24 (c) 23 (d) 28
  21. 21.What is the 17th term of the AP 7, 10, 13, 16, …? (a) 51 (b) 55 (c) 58 (d) 48
  22. 22.Which term of the AP 20, 25, 30, 35, … is 70? (a) 14th (b) 12th (c) 11th (d) 10th
  23. 23.What is the sum of all the whole numbers from 1 to 33? (a) 528 (b) 562 (c) 1122 (d) 561
  24. 24.What is the 14th term of the AP 1, 4, 7, 10, …? (a) 39 (b) 43 (c) 42 (d) 40
  25. 25.What is the missing term in the AP 2, ?, 10, 14, 18? (a) 10 (b) 7 (c) 5 (d) 6
  26. 26.Which term of the AP 4, 12, 20, 28, … is 148? (a) 20th (b) 18th (c) 21st (d) 19th
  27. 27.What is the 32nd term of the AP 19, 28, 37, 46, …? (a) 307 (b) 288 (c) 298 (d) 279
  28. 28.What is the 31st term of the AP 7, 16, 25, 34, …? (a) 270 (b) 286 (c) 277 (d) 279
  29. 29.What is the 40th term of the AP 8, 17, 26, 35, …? (a) 359 (b) 360 (c) 368 (d) 351
  30. 30.What is the 37th term of the AP 17, 24, 31, 38, …? (a) 259 (b) 252 (c) 269 (d) 276
  31. 31.What is the 12th term of the AP 11, 16, 21, 26, …? (a) 71 (b) 60 (c) 55 (d) 66
  32. 32.What is the 36th term of the AP 7, 14, 21, 28, …? (a) 253 (b) 259 (c) 252 (d) 245
  33. 33.What is the sum of all the whole numbers from 1 to 10? (a) 110 (b) 50 (c) 45 (d) 55
  34. 34.What is the sum of all the whole numbers from 1 to 81? (a) 3322 (b) 6642 (c) 3321 (d) 3240
  35. 35.What is the sum of the first 12 terms of the AP 1, 7, 13, …? (a) 67 (b) 408 (c) 816 (d) 444
  36. 36.What is the sum of the first 6 terms of the AP 7, 11, 15, …? (a) 27 (b) 114 (c) 204 (d) 102
  37. 37.What is the sum of the first 10 terms of the AP 4, 9, 14, …? (a) 530 (b) 265 (c) 49 (d) 290
  38. 38.What is the sum of all the whole numbers from 1 to 98? (a) 4802 (b) 9702 (c) 4753 (d) 4851
  39. 39.What is the sum of the first 10 terms of the AP 6, 9, 12, …? (a) 210 (b) 195 (c) 390 (d) 33
  40. 40.What is the 33rd term of the AP 3, 11, 19, 27, …? (a) 267 (b) 264 (c) 259 (d) 256

Answer key

  1. 3
  2. 110
  3. 86
  4. 20th
  5. 223
  6. 1770
  7. 15th
  8. 115
  9. 625
  10. 67
  11. 361
  12. 96
  13. 176
  14. 121
  15. 400
  16. 192
  17. 137
  18. 28
  19. 90
  20. 23
  21. 55
  22. 11th
  23. 561
  24. 40
  25. 6
  26. 19th
  27. 298
  28. 277
  29. 359
  30. 269
  31. 66
  32. 252
  33. 55
  34. 3321
  35. 408
  36. 102
  37. 265
  38. 4851
  39. 195
  40. 259

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