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Arithmetic Progression Worksheet for Olympiad

Maths Olympiad topic 29: Sequences and AP · Set 735 · 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.Which term of the AP 2, 9, 16, 23, … is 254? (a) 39th (b) 38th (c) 37th (d) 36th
  2. 2.What is the missing term in the AP 8, ?, 16, 20, 24? (a) 13 (b) 12 (c) 16 (d) 11
  3. 3.What is the sum of the first 11 terms of the AP 8, 13, 18, …? (a) 368 (b) 726 (c) 363 (d) 58
  4. 4.What is the sum of the first 9 terms of the AP 3, 7, 11, …? (a) 35 (b) 342 (c) 171 (d) 189
  5. 5.Which term of the AP 8, 11, 14, 17, … is 35? (a) 11th (b) 12th (c) 10th (d) 9th
  6. 6.What is the sum of the first 5 terms of the AP 5, 10, 15, …? (a) 75 (b) 150 (c) 80 (d) 25
  7. 7.What is the sum of the first 11 terms of the AP 4, 6, 8, …? (a) 165 (b) 24 (c) 308 (d) 154
  8. 8.What is the sum of the first 6 terms of the AP 5, 6, 7, …? (a) 48 (b) 45 (c) 90 (d) 10
  9. 9.What is the sum of the first 20 odd numbers (1 + 3 + 5 + …)? (a) 210 (b) 400 (c) 39 (d) 420
  10. 10.What is the 33rd term of the AP 8, 15, 22, 29, …? (a) 224 (b) 232 (c) 231 (d) 239
  11. 11.What is the 37th term of the AP 13, 18, 23, 28, …? (a) 180 (b) 193 (c) 185 (d) 198
  12. 12.What is the 29th term of the AP 14, 17, 20, 23, …? (a) 98 (b) 101 (c) 87 (d) 84
  13. 13.What is the sum of the first 7 terms of the AP 1, 5, 9, …? (a) 91 (b) 25 (c) 105 (d) 182
  14. 14.What is the sum of the first 9 odd numbers (1 + 3 + 5 + …)? (a) 81 (b) 17 (c) 90 (d) 45
  15. 15.What is the sum of the first 11 terms of the AP 6, 8, 10, …? (a) 187 (b) 176 (c) 352 (d) 26
  16. 16.Which term of the AP 15, 22, 29, 36, … is 141? (a) 19th (b) 18th (c) 21st (d) 20th
  17. 17.What is the sum of all the whole numbers from 1 to 12? (a) 156 (b) 66 (c) 78 (d) 72
  18. 18.What is the sum of the first 7 terms of the AP 8, 14, 20, …? (a) 44 (b) 182 (c) 364 (d) 203
  19. 19.Which term of the AP 4, 7, 10, 13, … is 25? (a) 7th (b) 10th (c) 9th (d) 8th
  20. 20.What is the sum of all the whole numbers from 1 to 77? (a) 6006 (b) 2926 (c) 3003 (d) 3004
  21. 21.Which term of the AP 15, 22, 29, 36, … is 274? (a) 40th (b) 37th (c) 39th (d) 38th
  22. 22.What is the missing term in the AP 10, ?, 22, 28, 34? (a) 15 (b) 17 (c) 22 (d) 16
  23. 23.What is the 39th term of the AP 12, 20, 28, 36, …? (a) 304 (b) 316 (c) 312 (d) 324
  24. 24.What is the sum of the first 5 terms of the AP 7, 8, 9, …? (a) 11 (b) 45 (c) 90 (d) 46
  25. 25.What is the sum of the first 9 terms of the AP 3, 4, 5, …? (a) 64 (b) 126 (c) 63 (d) 11
  26. 26.What is the 15th term of the AP 14, 22, 30, 38, …? (a) 120 (b) 126 (c) 112 (d) 134
  27. 27.What is the sum of the first 7 terms of the AP 7, 10, 13, …? (a) 115 (b) 224 (c) 112 (d) 25
  28. 28.What is the missing term in the AP 16, 25, 34, ?, 52? (a) 43 (b) 52 (c) 44 (d) 42
  29. 29.What is the missing term in the AP 11, 14, 17, ?, 23? (a) 19 (b) 21 (c) 20 (d) 23
  30. 30.What is the sum of the first 7 terms of the AP 3, 9, 15, …? (a) 147 (b) 168 (c) 294 (d) 39
  31. 31.What is the 39th term of the AP 4, 10, 16, 22, …? (a) 228 (b) 232 (c) 238 (d) 234
  32. 32.What is the 12th term of the AP 7, 11, 15, 19, …? (a) 48 (b) 44 (c) 55 (d) 51
  33. 33.What is the sum of the first 5 odd numbers (1 + 3 + 5 + …)? (a) 9 (b) 15 (c) 30 (d) 25
  34. 34.What is the sum of the first 10 odd numbers (1 + 3 + 5 + …)? (a) 110 (b) 100 (c) 55 (d) 19
  35. 35.What is the sum of the first 5 terms of the AP 3, 5, 7, …? (a) 70 (b) 35 (c) 40 (d) 11
  36. 36.What is the sum of the first 9 terms of the AP 7, 8, 9, …? (a) 100 (b) 198 (c) 99 (d) 15
  37. 37.What is the sum of the first 23 odd numbers (1 + 3 + 5 + …)? (a) 552 (b) 45 (c) 529 (d) 276
  38. 38.What is the sum of the first 11 terms of the AP 7, 10, 13, …? (a) 242 (b) 37 (c) 245 (d) 484
  39. 39.What is the sum of the first 30 odd numbers (1 + 3 + 5 + …)? (a) 465 (b) 930 (c) 59 (d) 900
  40. 40.What is the sum of all the whole numbers from 1 to 63? (a) 4032 (b) 2017 (c) 1953 (d) 2016

Answer key

  1. 37th
  2. 12
  3. 363
  4. 171
  5. 10th
  6. 75
  7. 154
  8. 45
  9. 400
  10. 232
  11. 193
  12. 98
  13. 91
  14. 81
  15. 176
  16. 19th
  17. 78
  18. 182
  19. 8th
  20. 3003
  21. 38th
  22. 16
  23. 316
  24. 45
  25. 63
  26. 126
  27. 112
  28. 43
  29. 20
  30. 147
  31. 232
  32. 51
  33. 25
  34. 100
  35. 35
  36. 99
  37. 529
  38. 242
  39. 900
  40. 2016

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