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Arithmetic Progression Worksheet for Olympiad

Maths Olympiad topic 29: Sequences and AP · Set 897 · 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 sum of the first 11 terms of the AP 10, 13, 16, …? (a) 275 (b) 278 (c) 40 (d) 550
  2. 2.What is the sum of the first 11 terms of the AP 4, 7, 10, …? (a) 34 (b) 209 (c) 212 (d) 418
  3. 3.What is the missing term in the AP 1, 3, ?, 7, 9? (a) 7 (b) 5 (c) 4 (d) 6
  4. 4.Which term of the AP 8, 17, 26, 35, … is 134? (a) 17th (b) 16th (c) 15th (d) 14th
  5. 5.Which term of the AP 6, 8, 10, 12, … is 82? (a) 38th (b) 41st (c) 40th (d) 39th
  6. 6.Which term of the AP 3, 9, 15, 21, … is 189? (a) 31st (b) 33rd (c) 34th (d) 32nd
  7. 7.What is the 39th term of the AP 16, 22, 28, 34, …? (a) 234 (b) 228 (c) 244 (d) 250
  8. 8.What is the sum of the first 9 terms of the AP 4, 10, 16, …? (a) 252 (b) 279 (c) 504 (d) 52
  9. 9.What is the sum of all the whole numbers from 1 to 97? (a) 4754 (b) 9506 (c) 4753 (d) 4656
  10. 10.What is the 18th term of the AP 15, 17, 19, 21, …? (a) 51 (b) 49 (c) 34 (d) 36
  11. 11.What is the 27th term of the AP 1, 3, 5, 7, …? (a) 53 (b) 52 (c) 54 (d) 55
  12. 12.What is the sum of the first 5 terms of the AP 9, 10, 11, …? (a) 55 (b) 56 (c) 110 (d) 13
  13. 13.Which term of the AP 18, 24, 30, 36, … is 234? (a) 37th (b) 39th (c) 38th (d) 36th
  14. 14.What is the sum of the first 11 terms of the AP 7, 10, 13, …? (a) 245 (b) 37 (c) 484 (d) 242
  15. 15.Which term of the AP 19, 22, 25, 28, … is 58? (a) 16th (b) 14th (c) 15th (d) 13th
  16. 16.What is the sum of the first 5 terms of the AP 3, 8, 13, …? (a) 23 (b) 130 (c) 70 (d) 65
  17. 17.What is the missing term in the AP 17, ?, 33, 41, 49? (a) 26 (b) 25 (c) 24 (d) 33
  18. 18.What is the sum of all the whole numbers from 1 to 67? (a) 2211 (b) 2279 (c) 4556 (d) 2278
  19. 19.What is the 36th term of the AP 6, 14, 22, 30, …? (a) 288 (b) 294 (c) 280 (d) 286
  20. 20.What is the missing term in the AP 11, 20, ?, 38, 47? (a) 30 (b) 38 (c) 29 (d) 28
  21. 21.What is the sum of the first 8 terms of the AP 5, 6, 7, …? (a) 136 (b) 12 (c) 68 (d) 72
  22. 22.What is the sum of the first 23 odd numbers (1 + 3 + 5 + …)? (a) 552 (b) 529 (c) 45 (d) 276
  23. 23.What is the sum of the first 15 odd numbers (1 + 3 + 5 + …)? (a) 240 (b) 120 (c) 225 (d) 29
  24. 24.What is the sum of the first 12 terms of the AP 9, 10, 11, …? (a) 348 (b) 20 (c) 180 (d) 174
  25. 25.What is the sum of the first 6 terms of the AP 1, 7, 13, …? (a) 31 (b) 114 (c) 192 (d) 96
  26. 26.What is the sum of the first 10 odd numbers (1 + 3 + 5 + …)? (a) 55 (b) 110 (c) 100 (d) 19
  27. 27.What is the 12th term of the AP 9, 18, 27, 36, …? (a) 99 (b) 109 (c) 108 (d) 117
  28. 28.Which term of the AP 7, 9, 11, 13, … is 39? (a) 19th (b) 18th (c) 17th (d) 16th
  29. 29.What is the 35th term of the AP 2, 4, 6, 8, …? (a) 71 (b) 70 (c) 72 (d) 68
  30. 30.What is the sum of the first 9 terms of the AP 8, 9, 10, …? (a) 16 (b) 108 (c) 216 (d) 109
  31. 31.What is the sum of the first 10 terms of the AP 2, 8, 14, …? (a) 320 (b) 290 (c) 56 (d) 580
  32. 32.What is the sum of the first 17 odd numbers (1 + 3 + 5 + …)? (a) 33 (b) 153 (c) 289 (d) 306
  33. 33.What is the sum of the first 9 odd numbers (1 + 3 + 5 + …)? (a) 81 (b) 90 (c) 45 (d) 17
  34. 34.What is the sum of the first 24 odd numbers (1 + 3 + 5 + …)? (a) 576 (b) 600 (c) 300 (d) 47
  35. 35.What is the sum of all the whole numbers from 1 to 22? (a) 242 (b) 231 (c) 253 (d) 506
  36. 36.What is the 39th term of the AP 10, 16, 22, 28, …? (a) 238 (b) 234 (c) 244 (d) 228
  37. 37.What is the 33rd term of the AP 7, 9, 11, 13, …? (a) 66 (b) 64 (c) 71 (d) 73
  38. 38.What is the missing term in the AP 8, 17, 26, ?, 44? (a) 35 (b) 36 (c) 44 (d) 34
  39. 39.What is the sum of the first 18 odd numbers (1 + 3 + 5 + …)? (a) 342 (b) 171 (c) 324 (d) 35
  40. 40.What is the 20th term of the AP 11, 18, 25, 32, …? (a) 133 (b) 151 (c) 144 (d) 140

Answer key

  1. 275
  2. 209
  3. 5
  4. 15th
  5. 39th
  6. 32nd
  7. 244
  8. 252
  9. 4753
  10. 49
  11. 53
  12. 55
  13. 37th
  14. 242
  15. 14th
  16. 65
  17. 25
  18. 2278
  19. 286
  20. 29
  21. 68
  22. 529
  23. 225
  24. 174
  25. 96
  26. 100
  27. 108
  28. 17th
  29. 70
  30. 108
  31. 290
  32. 289
  33. 81
  34. 576
  35. 253
  36. 238
  37. 71
  38. 35
  39. 324
  40. 144

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