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Arithmetic Progression Worksheet for Olympiad

Maths Olympiad topic 29: Sequences and AP · Set 401 · 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 missing term in the AP 9, 17, ?, 33, 41? (a) 33 (b) 26 (c) 24 (d) 25
  2. 2.Which term of the AP 13, 18, 23, 28, … is 178? (a) 36th (b) 34th (c) 33rd (d) 35th
  3. 3.What is the sum of the first 12 terms of the AP 1, 5, 9, …? (a) 552 (b) 276 (c) 300 (d) 45
  4. 4.What is the missing term in the AP 2, 4, 6, ?, 10? (a) 10 (b) 7 (c) 9 (d) 8
  5. 5.What is the missing term in the AP 19, 21, ?, 25, 27? (a) 25 (b) 22 (c) 23 (d) 24
  6. 6.What is the 38th term of the AP 1, 10, 19, 28, …? (a) 343 (b) 334 (c) 333 (d) 342
  7. 7.What is the sum of the first 23 odd numbers (1 + 3 + 5 + …)? (a) 552 (b) 529 (c) 276 (d) 45
  8. 8.What is the sum of the first 9 terms of the AP 7, 10, 13, …? (a) 174 (b) 31 (c) 171 (d) 342
  9. 9.What is the sum of the first 5 odd numbers (1 + 3 + 5 + …)? (a) 30 (b) 15 (c) 9 (d) 25
  10. 10.Which term of the AP 15, 18, 21, 24, … is 108? (a) 36th (b) 33rd (c) 31st (d) 32nd
  11. 11.What is the sum of the first 11 terms of the AP 2, 7, 12, …? (a) 302 (b) 297 (c) 594 (d) 52
  12. 12.What is the sum of the first 9 odd numbers (1 + 3 + 5 + …)? (a) 17 (b) 45 (c) 90 (d) 81
  13. 13.What is the sum of all the whole numbers from 1 to 34? (a) 1190 (b) 578 (c) 595 (d) 561
  14. 14.What is the missing term in the AP 18, 25, 32, ?, 46? (a) 38 (b) 40 (c) 46 (d) 39
  15. 15.What is the sum of the first 7 odd numbers (1 + 3 + 5 + …)? (a) 56 (b) 13 (c) 49 (d) 28
  16. 16.What is the sum of the first 9 terms of the AP 8, 9, 10, …? (a) 16 (b) 109 (c) 216 (d) 108
  17. 17.What is the 12th term of the AP 2, 5, 8, 11, …? (a) 38 (b) 33 (c) 36 (d) 35
  18. 18.What is the missing term in the AP 13, ?, 31, 40, 49? (a) 23 (b) 31 (c) 22 (d) 21
  19. 19.What is the sum of the first 15 odd numbers (1 + 3 + 5 + …)? (a) 120 (b) 29 (c) 240 (d) 225
  20. 20.What is the sum of the first 7 terms of the AP 5, 6, 7, …? (a) 112 (b) 57 (c) 11 (d) 56
  21. 21.What is the 15th term of the AP 17, 26, 35, 44, …? (a) 135 (b) 126 (c) 143 (d) 152
  22. 22.Which term of the AP 17, 23, 29, 35, … is 215? (a) 33rd (b) 35th (c) 34th (d) 36th
  23. 23.What is the sum of the first 5 terms of the AP 5, 6, 7, …? (a) 70 (b) 35 (c) 9 (d) 36
  24. 24.What is the missing term in the AP 1, ?, 7, 10, 13? (a) 5 (b) 3 (c) 7 (d) 4
  25. 25.What is the 36th term of the AP 1, 6, 11, 16, …? (a) 181 (b) 180 (c) 176 (d) 175
  26. 26.What is the missing term in the AP 4, 6, ?, 10, 12? (a) 7 (b) 8 (c) 10 (d) 9
  27. 27.What is the sum of the first 9 terms of the AP 8, 11, 14, …? (a) 180 (b) 32 (c) 183 (d) 360
  28. 28.What is the 19th term of the AP 16, 20, 24, 28, …? (a) 72 (b) 88 (c) 92 (d) 76
  29. 29.What is the 27th term of the AP 1, 4, 7, 10, …? (a) 81 (b) 78 (c) 79 (d) 82
  30. 30.What is the 25th term of the AP 3, 11, 19, 27, …? (a) 200 (b) 192 (c) 195 (d) 203
  31. 31.What is the sum of the first 22 odd numbers (1 + 3 + 5 + …)? (a) 43 (b) 253 (c) 506 (d) 484
  32. 32.Which term of the AP 11, 14, 17, 20, … is 71? (a) 20th (b) 21st (c) 22nd (d) 23rd
  33. 33.What is the sum of the first 9 terms of the AP 3, 8, 13, …? (a) 414 (b) 212 (c) 207 (d) 43
  34. 34.Which term of the AP 6, 13, 20, 27, … is 97? (a) 16th (b) 14th (c) 15th (d) 13th
  35. 35.Which term of the AP 5, 14, 23, 32, … is 131? (a) 14th (b) 17th (c) 16th (d) 15th
  36. 36.What is the sum of the first 9 terms of the AP 3, 5, 7, …? (a) 198 (b) 108 (c) 99 (d) 19
  37. 37.What is the 24th term of the AP 10, 16, 22, 28, …? (a) 144 (b) 148 (c) 154 (d) 138
  38. 38.What is the sum of all the whole numbers from 1 to 91? (a) 4095 (b) 4186 (c) 4187 (d) 8372
  39. 39.What is the 36th term of the AP 11, 13, 15, 17, …? (a) 83 (b) 70 (c) 81 (d) 72
  40. 40.What is the sum of the first 25 odd numbers (1 + 3 + 5 + …)? (a) 49 (b) 325 (c) 625 (d) 650

Answer key

  1. 25
  2. 34th
  3. 276
  4. 8
  5. 23
  6. 334
  7. 529
  8. 171
  9. 25
  10. 32nd
  11. 297
  12. 81
  13. 595
  14. 39
  15. 49
  16. 108
  17. 35
  18. 22
  19. 225
  20. 56
  21. 143
  22. 34th
  23. 35
  24. 4
  25. 176
  26. 8
  27. 180
  28. 88
  29. 79
  30. 195
  31. 484
  32. 21st
  33. 207
  34. 14th
  35. 15th
  36. 99
  37. 148
  38. 4186
  39. 81
  40. 625

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