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Arithmetic Progression Worksheet for Olympiad

Maths Olympiad topic 29: Sequences and AP · Set 940 · 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 all the whole numbers from 1 to 72? (a) 5256 (b) 2556 (c) 2628 (d) 2592
  2. 2.What is the 22nd term of the AP 4, 13, 22, 31, …? (a) 198 (b) 202 (c) 189 (d) 193
  3. 3.What is the 33rd term of the AP 4, 10, 16, 22, …? (a) 196 (b) 202 (c) 198 (d) 192
  4. 4.What is the sum of the first 19 odd numbers (1 + 3 + 5 + …)? (a) 361 (b) 37 (c) 380 (d) 190
  5. 5.What is the sum of all the whole numbers from 1 to 49? (a) 1226 (b) 1225 (c) 2450 (d) 1176
  6. 6.What is the missing term in the AP 10, ?, 24, 31, 38? (a) 17 (b) 16 (c) 24 (d) 18
  7. 7.What is the 28th term of the AP 7, 12, 17, 22, …? (a) 147 (b) 135 (c) 142 (d) 140
  8. 8.Which term of the AP 5, 11, 17, 23, … is 65? (a) 10th (b) 13th (c) 12th (d) 11th
  9. 9.What is the missing term in the AP 9, ?, 27, 36, 45? (a) 18 (b) 19 (c) 27 (d) 17
  10. 10.What is the sum of the first 21 odd numbers (1 + 3 + 5 + …)? (a) 462 (b) 41 (c) 441 (d) 231
  11. 11.Which term of the AP 11, 19, 27, 35, … is 315? (a) 40th (b) 39th (c) 38th (d) 41st
  12. 12.What is the sum of the first 7 terms of the AP 1, 2, 3, …? (a) 28 (b) 7 (c) 29 (d) 56
  13. 13.Which term of the AP 8, 15, 22, 29, … is 64? (a) 10th (b) 8th (c) 11th (d) 9th
  14. 14.What is the 24th term of the AP 12, 15, 18, 21, …? (a) 84 (b) 69 (c) 72 (d) 81
  15. 15.What is the sum of the first 13 odd numbers (1 + 3 + 5 + …)? (a) 91 (b) 182 (c) 25 (d) 169
  16. 16.What is the sum of all the whole numbers from 1 to 23? (a) 277 (b) 276 (c) 552 (d) 253
  17. 17.What is the sum of the first 5 terms of the AP 8, 11, 14, …? (a) 73 (b) 70 (c) 140 (d) 20
  18. 18.What is the sum of the first 6 terms of the AP 5, 6, 7, …? (a) 48 (b) 90 (c) 10 (d) 45
  19. 19.What is the sum of the first 29 odd numbers (1 + 3 + 5 + …)? (a) 870 (b) 841 (c) 435 (d) 57
  20. 20.What is the missing term in the AP 10, ?, 22, 28, 34? (a) 15 (b) 17 (c) 16 (d) 22
  21. 21.What is the sum of the first 9 terms of the AP 4, 9, 14, …? (a) 221 (b) 44 (c) 216 (d) 432
  22. 22.What is the sum of the first 25 odd numbers (1 + 3 + 5 + …)? (a) 650 (b) 325 (c) 49 (d) 625
  23. 23.What is the 14th term of the AP 16, 25, 34, 43, …? (a) 117 (b) 142 (c) 133 (d) 126
  24. 24.What is the sum of the first 15 odd numbers (1 + 3 + 5 + …)? (a) 120 (b) 29 (c) 225 (d) 240
  25. 25.What is the sum of the first 16 odd numbers (1 + 3 + 5 + …)? (a) 256 (b) 31 (c) 272 (d) 136
  26. 26.What is the sum of the first 9 odd numbers (1 + 3 + 5 + …)? (a) 81 (b) 45 (c) 90 (d) 17
  27. 27.What is the sum of the first 11 terms of the AP 7, 9, 11, …? (a) 27 (b) 187 (c) 374 (d) 198
  28. 28.What is the 19th term of the AP 11, 17, 23, 29, …? (a) 125 (b) 119 (c) 108 (d) 114
  29. 29.What is the sum of the first 5 terms of the AP 1, 2, 3, …? (a) 16 (b) 5 (c) 15 (d) 30
  30. 30.What is the 21st term of the AP 10, 18, 26, 34, …? (a) 160 (b) 178 (c) 170 (d) 168
  31. 31.What is the sum of the first 6 terms of the AP 10, 12, 14, …? (a) 20 (b) 96 (c) 90 (d) 180
  32. 32.What is the 16th term of the AP 9, 12, 15, 18, …? (a) 48 (b) 45 (c) 54 (d) 57
  33. 33.What is the 22nd term of the AP 5, 12, 19, 26, …? (a) 159 (b) 152 (c) 147 (d) 154
  34. 34.Which term of the AP 15, 19, 23, 27, … is 143? (a) 32nd (b) 35th (c) 34th (d) 33rd
  35. 35.Which term of the AP 6, 12, 18, 24, … is 60? (a) 9th (b) 12th (c) 10th (d) 11th
  36. 36.What is the sum of the first 7 odd numbers (1 + 3 + 5 + …)? (a) 28 (b) 49 (c) 13 (d) 56
  37. 37.Which term of the AP 6, 12, 18, 24, … is 96? (a) 17th (b) 16th (c) 18th (d) 15th
  38. 38.What is the sum of the first 6 terms of the AP 1, 5, 9, …? (a) 132 (b) 21 (c) 66 (d) 78
  39. 39.What is the 36th term of the AP 19, 21, 23, 25, …? (a) 89 (b) 70 (c) 72 (d) 91
  40. 40.What is the missing term in the AP 15, 22, 29, ?, 43? (a) 35 (b) 36 (c) 43 (d) 37

Answer key

  1. 2628
  2. 193
  3. 196
  4. 361
  5. 1225
  6. 17
  7. 142
  8. 11th
  9. 18
  10. 441
  11. 39th
  12. 28
  13. 9th
  14. 81
  15. 169
  16. 276
  17. 70
  18. 45
  19. 841
  20. 16
  21. 216
  22. 625
  23. 133
  24. 225
  25. 256
  26. 81
  27. 187
  28. 119
  29. 15
  30. 170
  31. 90
  32. 54
  33. 152
  34. 33rd
  35. 10th
  36. 49
  37. 16th
  38. 66
  39. 89
  40. 36

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