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Arithmetic Progression Worksheet for Olympiad

Maths Olympiad topic 29: Sequences and AP · Set 920 · 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 5 terms of the AP 3, 6, 9, …? (a) 90 (b) 45 (c) 48 (d) 15
  2. 2.Which term of the AP 6, 10, 14, 18, … is 78? (a) 20th (b) 19th (c) 21st (d) 18th
  3. 3.What is the sum of the first 15 odd numbers (1 + 3 + 5 + …)? (a) 29 (b) 225 (c) 240 (d) 120
  4. 4.Which term of the AP 15, 19, 23, 27, … is 95? (a) 20th (b) 21st (c) 22nd (d) 23rd
  5. 5.What is the missing term in the AP 6, ?, 16, 21, 26? (a) 12 (b) 10 (c) 16 (d) 11
  6. 6.What is the sum of the first 13 odd numbers (1 + 3 + 5 + …)? (a) 25 (b) 169 (c) 182 (d) 91
  7. 7.What is the sum of the first 8 terms of the AP 3, 6, 9, …? (a) 216 (b) 108 (c) 120 (d) 24
  8. 8.What is the missing term in the AP 4, 12, ?, 28, 36? (a) 20 (b) 21 (c) 19 (d) 28
  9. 9.What is the 29th term of the AP 19, 23, 27, 31, …? (a) 112 (b) 131 (c) 116 (d) 135
  10. 10.What is the missing term in the AP 8, 14, 20, ?, 32? (a) 27 (b) 26 (c) 32 (d) 25
  11. 11.Which term of the AP 11, 14, 17, 20, … is 95? (a) 30th (b) 28th (c) 31st (d) 29th
  12. 12.What is the sum of the first 8 terms of the AP 8, 9, 10, …? (a) 15 (b) 184 (c) 92 (d) 96
  13. 13.Which term of the AP 14, 16, 18, 20, … is 46? (a) 23rd (b) 17th (c) 18th (d) 16th
  14. 14.What is the sum of the first 30 odd numbers (1 + 3 + 5 + …)? (a) 465 (b) 59 (c) 900 (d) 930
  15. 15.What is the sum of the first 9 odd numbers (1 + 3 + 5 + …)? (a) 45 (b) 81 (c) 90 (d) 17
  16. 16.Which term of the AP 17, 20, 23, 26, … is 95? (a) 26th (b) 28th (c) 27th (d) 29th
  17. 17.What is the missing term in the AP 16, 22, 28, ?, 40? (a) 34 (b) 35 (c) 40 (d) 33
  18. 18.What is the sum of the first 29 odd numbers (1 + 3 + 5 + …)? (a) 870 (b) 841 (c) 57 (d) 435
  19. 19.What is the 28th term of the AP 4, 12, 20, 28, …? (a) 220 (b) 216 (c) 228 (d) 224
  20. 20.What is the 29th term of the AP 1, 9, 17, 25, …? (a) 225 (b) 224 (c) 232 (d) 233
  21. 21.What is the 22nd term of the AP 7, 13, 19, 25, …? (a) 126 (b) 132 (c) 133 (d) 139
  22. 22.What is the sum of all the whole numbers from 1 to 45? (a) 2070 (b) 990 (c) 1035 (d) 1036
  23. 23.What is the 34th term of the AP 15, 24, 33, 42, …? (a) 306 (b) 312 (c) 297 (d) 321
  24. 24.What is the 32nd term of the AP 12, 15, 18, 21, …? (a) 108 (b) 96 (c) 93 (d) 105
  25. 25.What is the 19th term of the AP 11, 17, 23, 29, …? (a) 108 (b) 125 (c) 119 (d) 114
  26. 26.What is the sum of all the whole numbers from 1 to 31? (a) 496 (b) 465 (c) 992 (d) 497
  27. 27.What is the missing term in the AP 20, 24, ?, 32, 36? (a) 27 (b) 29 (c) 32 (d) 28
  28. 28.Which term of the AP 1, 5, 9, 13, … is 53? (a) 14th (b) 16th (c) 15th (d) 13th
  29. 29.What is the sum of the first 6 terms of the AP 5, 9, 13, …? (a) 90 (b) 180 (c) 102 (d) 25
  30. 30.What is the sum of the first 22 odd numbers (1 + 3 + 5 + …)? (a) 484 (b) 253 (c) 506 (d) 43
  31. 31.What is the missing term in the AP 19, ?, 35, 43, 51? (a) 35 (b) 26 (c) 28 (d) 27
  32. 32.What is the missing term in the AP 20, 25, 30, ?, 40? (a) 34 (b) 36 (c) 35 (d) 40
  33. 33.What is the 28th term of the AP 15, 21, 27, 33, …? (a) 168 (b) 183 (c) 177 (d) 162
  34. 34.What is the sum of the first 5 terms of the AP 3, 7, 11, …? (a) 65 (b) 19 (c) 110 (d) 55
  35. 35.What is the 12th term of the AP 20, 29, 38, 47, …? (a) 99 (b) 128 (c) 119 (d) 108
  36. 36.What is the 34th term of the AP 13, 19, 25, 31, …? (a) 198 (b) 217 (c) 211 (d) 204
  37. 37.Which term of the AP 14, 17, 20, 23, … is 128? (a) 40th (b) 41st (c) 39th (d) 38th
  38. 38.What is the 15th term of the AP 8, 16, 24, 32, …? (a) 120 (b) 112 (c) 121 (d) 128
  39. 39.What is the 15th term of the AP 20, 28, 36, 44, …? (a) 112 (b) 132 (c) 140 (d) 120
  40. 40.What is the sum of all the whole numbers from 1 to 36? (a) 1332 (b) 666 (c) 648 (d) 630

Answer key

  1. 45
  2. 19th
  3. 225
  4. 21st
  5. 11
  6. 169
  7. 108
  8. 20
  9. 131
  10. 26
  11. 29th
  12. 92
  13. 17th
  14. 900
  15. 81
  16. 27th
  17. 34
  18. 841
  19. 220
  20. 225
  21. 133
  22. 1035
  23. 312
  24. 105
  25. 119
  26. 496
  27. 28
  28. 14th
  29. 90
  30. 484
  31. 27
  32. 35
  33. 177
  34. 55
  35. 119
  36. 211
  37. 39th
  38. 120
  39. 132
  40. 666

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