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Arithmetic Progression Worksheet for Olympiad

Maths Olympiad topic 29: Sequences and AP · Set 866 · 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 20th term of the AP 5, 7, 9, 11, …? (a) 45 (b) 40 (c) 43 (d) 38
  2. 2.What is the sum of the first 7 terms of the AP 6, 10, 14, …? (a) 30 (b) 252 (c) 126 (d) 140
  3. 3.What is the sum of the first 12 odd numbers (1 + 3 + 5 + …)? (a) 23 (b) 156 (c) 144 (d) 78
  4. 4.What is the 21st term of the AP 6, 12, 18, 24, …? (a) 132 (b) 120 (c) 126 (d) 127
  5. 5.What is the 24th term of the AP 20, 23, 26, 29, …? (a) 92 (b) 69 (c) 72 (d) 89
  6. 6.Which term of the AP 17, 19, 21, 23, … is 45? (a) 15th (b) 14th (c) 17th (d) 16th
  7. 7.What is the sum of all the whole numbers from 1 to 78? (a) 6162 (b) 3003 (c) 3081 (d) 3042
  8. 8.What is the 32nd term of the AP 4, 9, 14, 19, …? (a) 164 (b) 159 (c) 155 (d) 160
  9. 9.What is the 29th term of the AP 14, 18, 22, 26, …? (a) 130 (b) 126 (c) 112 (d) 116
  10. 10.What is the sum of the first 11 terms of the AP 4, 7, 10, …? (a) 212 (b) 34 (c) 418 (d) 209
  11. 11.Which term of the AP 3, 11, 19, 27, … is 227? (a) 28th (b) 31st (c) 30th (d) 29th
  12. 12.What is the 16th term of the AP 12, 15, 18, 21, …? (a) 48 (b) 45 (c) 57 (d) 60
  13. 13.Which term of the AP 14, 22, 30, 38, … is 134? (a) 15th (b) 16th (c) 18th (d) 17th
  14. 14.What is the 23rd term of the AP 16, 19, 22, 25, …? (a) 85 (b) 82 (c) 69 (d) 66
  15. 15.What is the 19th term of the AP 7, 11, 15, 19, …? (a) 76 (b) 83 (c) 72 (d) 79
  16. 16.Which term of the AP 18, 25, 32, 39, … is 109? (a) 16th (b) 13th (c) 14th (d) 15th
  17. 17.What is the sum of the first 8 terms of the AP 4, 6, 8, …? (a) 18 (b) 96 (c) 176 (d) 88
  18. 18.What is the sum of the first 10 terms of the AP 5, 8, 11, …? (a) 200 (b) 32 (c) 185 (d) 370
  19. 19.What is the 17th term of the AP 2, 6, 10, 14, …? (a) 66 (b) 70 (c) 64 (d) 68
  20. 20.What is the 17th term of the AP 3, 8, 13, 18, …? (a) 83 (b) 85 (c) 88 (d) 80
  21. 21.What is the 31st term of the AP 14, 21, 28, 35, …? (a) 231 (b) 224 (c) 217 (d) 210
  22. 22.What is the sum of the first 11 terms of the AP 8, 11, 14, …? (a) 38 (b) 506 (c) 253 (d) 256
  23. 23.What is the 35th term of the AP 14, 22, 30, 38, …? (a) 272 (b) 294 (c) 280 (d) 286
  24. 24.What is the 33rd term of the AP 8, 13, 18, 23, …? (a) 165 (b) 173 (c) 168 (d) 160
  25. 25.Which term of the AP 15, 17, 19, 21, … is 81? (a) 34th (b) 36th (c) 35th (d) 33rd
  26. 26.What is the sum of the first 10 terms of the AP 1, 2, 3, …? (a) 10 (b) 110 (c) 55 (d) 60
  27. 27.What is the sum of the first 11 terms of the AP 1, 6, 11, …? (a) 291 (b) 286 (c) 51 (d) 572
  28. 28.What is the sum of the first 6 terms of the AP 4, 10, 16, …? (a) 132 (b) 228 (c) 34 (d) 114
  29. 29.What is the 27th term of the AP 11, 16, 21, 26, …? (a) 141 (b) 130 (c) 146 (d) 135
  30. 30.What is the 21st term of the AP 14, 23, 32, 41, …? (a) 180 (b) 194 (c) 189 (d) 203
  31. 31.What is the 17th term of the AP 19, 27, 35, 43, …? (a) 128 (b) 155 (c) 136 (d) 147
  32. 32.What is the missing term in the AP 6, 14, ?, 30, 38? (a) 30 (b) 22 (c) 21 (d) 23
  33. 33.What is the 35th term of the AP 12, 19, 26, 33, …? (a) 257 (b) 238 (c) 245 (d) 250
  34. 34.What is the sum of all the whole numbers from 1 to 99? (a) 4951 (b) 4851 (c) 4950 (d) 9900
  35. 35.What is the sum of the first 8 terms of the AP 1, 2, 3, …? (a) 36 (b) 8 (c) 40 (d) 72
  36. 36.What is the sum of the first 10 terms of the AP 10, 15, 20, …? (a) 55 (b) 325 (c) 350 (d) 650
  37. 37.What is the 16th term of the AP 12, 16, 20, 24, …? (a) 76 (b) 72 (c) 60 (d) 64
  38. 38.What is the sum of the first 9 terms of the AP 10, 12, 14, …? (a) 324 (b) 26 (c) 171 (d) 162
  39. 39.What is the sum of the first 29 odd numbers (1 + 3 + 5 + …)? (a) 435 (b) 57 (c) 841 (d) 870
  40. 40.What is the 34th term of the AP 6, 8, 10, 12, …? (a) 74 (b) 72 (c) 68 (d) 66

Answer key

  1. 43
  2. 126
  3. 144
  4. 126
  5. 89
  6. 15th
  7. 3081
  8. 159
  9. 126
  10. 209
  11. 29th
  12. 57
  13. 16th
  14. 82
  15. 79
  16. 14th
  17. 88
  18. 185
  19. 66
  20. 83
  21. 224
  22. 253
  23. 286
  24. 168
  25. 34th
  26. 55
  27. 286
  28. 114
  29. 141
  30. 194
  31. 147
  32. 22
  33. 250
  34. 4950
  35. 36
  36. 325
  37. 72
  38. 162
  39. 841
  40. 72

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