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Arithmetic Progression Worksheet for Olympiad

Maths Olympiad topic 29: Sequences and AP · Set 852 · 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 10th term of the AP 17, 19, 21, 23, …? (a) 18 (b) 37 (c) 20 (d) 35
  2. 2.What is the 12th term of the AP 20, 28, 36, 44, …? (a) 116 (b) 88 (c) 108 (d) 96
  3. 3.What is the missing term in the AP 18, 24, ?, 36, 42? (a) 31 (b) 36 (c) 29 (d) 30
  4. 4.What is the sum of all the whole numbers from 1 to 67? (a) 2211 (b) 2278 (c) 4556 (d) 2279
  5. 5.What is the sum of all the whole numbers from 1 to 81? (a) 3321 (b) 6642 (c) 3240 (d) 3322
  6. 6.What is the 29th term of the AP 5, 11, 17, 23, …? (a) 179 (b) 174 (c) 168 (d) 173
  7. 7.What is the sum of the first 12 terms of the AP 10, 13, 16, …? (a) 336 (b) 636 (c) 43 (d) 318
  8. 8.What is the sum of the first 11 terms of the AP 9, 11, 13, …? (a) 220 (b) 209 (c) 29 (d) 418
  9. 9.What is the sum of the first 5 terms of the AP 10, 15, 20, …? (a) 200 (b) 100 (c) 105 (d) 30
  10. 10.What is the sum of the first 6 terms of the AP 6, 10, 14, …? (a) 96 (b) 26 (c) 192 (d) 108
  11. 11.What is the sum of the first 7 terms of the AP 5, 6, 7, …? (a) 56 (b) 57 (c) 112 (d) 11
  12. 12.Which term of the AP 11, 17, 23, 29, … is 107? (a) 19th (b) 16th (c) 18th (d) 17th
  13. 13.What is the sum of the first 8 odd numbers (1 + 3 + 5 + …)? (a) 15 (b) 64 (c) 72 (d) 36
  14. 14.What is the 21st term of the AP 7, 11, 15, 19, …? (a) 87 (b) 80 (c) 91 (d) 84
  15. 15.What is the missing term in the AP 5, ?, 17, 23, 29? (a) 12 (b) 10 (c) 11 (d) 17
  16. 16.What is the sum of the first 7 terms of the AP 10, 11, 12, …? (a) 182 (b) 92 (c) 91 (d) 16
  17. 17.What is the sum of the first 10 terms of the AP 9, 15, 21, …? (a) 720 (b) 360 (c) 63 (d) 390
  18. 18.Which term of the AP 2, 10, 18, 26, … is 106? (a) 13th (b) 15th (c) 14th (d) 16th
  19. 19.What is the 35th term of the AP 16, 22, 28, 34, …? (a) 204 (b) 226 (c) 220 (d) 210
  20. 20.What is the sum of all the whole numbers from 1 to 13? (a) 78 (b) 91 (c) 182 (d) 92
  21. 21.What is the sum of the first 6 terms of the AP 10, 15, 20, …? (a) 35 (b) 150 (c) 270 (d) 135
  22. 22.What is the 12th term of the AP 5, 14, 23, 32, …? (a) 113 (b) 99 (c) 104 (d) 108
  23. 23.What is the sum of the first 9 terms of the AP 10, 15, 20, …? (a) 50 (b) 275 (c) 270 (d) 540
  24. 24.Which term of the AP 18, 21, 24, 27, … is 39? (a) 9th (b) 7th (c) 8th (d) 13th
  25. 25.What is the sum of the first 20 odd numbers (1 + 3 + 5 + …)? (a) 420 (b) 210 (c) 39 (d) 400
  26. 26.What is the sum of the first 9 terms of the AP 3, 7, 11, …? (a) 189 (b) 35 (c) 171 (d) 342
  27. 27.What is the 29th term of the AP 10, 12, 14, 16, …? (a) 56 (b) 58 (c) 66 (d) 68
  28. 28.Which term of the AP 12, 19, 26, 33, … is 215? (a) 31st (b) 32nd (c) 30th (d) 29th
  29. 29.What is the sum of the first 7 terms of the AP 10, 16, 22, …? (a) 46 (b) 217 (c) 392 (d) 196
  30. 30.Which term of the AP 3, 9, 15, 21, … is 75? (a) 12th (b) 14th (c) 13th (d) 15th
  31. 31.What is the 23rd term of the AP 12, 18, 24, 30, …? (a) 150 (b) 132 (c) 138 (d) 144
  32. 32.What is the 11th term of the AP 6, 14, 22, 30, …? (a) 94 (b) 80 (c) 86 (d) 88
  33. 33.What is the sum of the first 6 terms of the AP 2, 3, 4, …? (a) 54 (b) 30 (c) 7 (d) 27
  34. 34.Which term of the AP 12, 21, 30, 39, … is 363? (a) 39th (b) 42nd (c) 41st (d) 40th
  35. 35.What is the sum of the first 12 terms of the AP 3, 6, 9, …? (a) 468 (b) 252 (c) 36 (d) 234
  36. 36.What is the sum of the first 14 odd numbers (1 + 3 + 5 + …)? (a) 27 (b) 210 (c) 105 (d) 196
  37. 37.What is the sum of the first 6 terms of the AP 1, 6, 11, …? (a) 26 (b) 81 (c) 96 (d) 162
  38. 38.What is the sum of the first 15 odd numbers (1 + 3 + 5 + …)? (a) 29 (b) 225 (c) 120 (d) 240
  39. 39.What is the sum of the first 10 terms of the AP 8, 12, 16, …? (a) 44 (b) 260 (c) 520 (d) 280
  40. 40.What is the 11th term of the AP 5, 14, 23, 32, …? (a) 90 (b) 99 (c) 95 (d) 104

Answer key

  1. 35
  2. 108
  3. 30
  4. 2278
  5. 3321
  6. 173
  7. 318
  8. 209
  9. 100
  10. 96
  11. 56
  12. 17th
  13. 64
  14. 87
  15. 11
  16. 91
  17. 360
  18. 14th
  19. 220
  20. 91
  21. 135
  22. 104
  23. 270
  24. 8th
  25. 400
  26. 171
  27. 66
  28. 30th
  29. 196
  30. 13th
  31. 144
  32. 86
  33. 27
  34. 40th
  35. 234
  36. 196
  37. 81
  38. 225
  39. 260
  40. 95

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