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Arithmetic Progression Worksheet for Olympiad

Maths Olympiad topic 29: Sequences and AP · Set 743 · 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 29th term of the AP 4, 13, 22, 31, …? (a) 265 (b) 261 (c) 252 (d) 256
  2. 2.What is the sum of the first 11 terms of the AP 9, 14, 19, …? (a) 59 (b) 748 (c) 379 (d) 374
  3. 3.Which term of the AP 16, 21, 26, 31, … is 196? (a) 39th (b) 38th (c) 37th (d) 36th
  4. 4.What is the sum of the first 12 terms of the AP 8, 9, 10, …? (a) 324 (b) 168 (c) 162 (d) 19
  5. 5.What is the sum of the first 5 odd numbers (1 + 3 + 5 + …)? (a) 9 (b) 30 (c) 15 (d) 25
  6. 6.What is the 29th term of the AP 16, 19, 22, 25, …? (a) 100 (b) 103 (c) 84 (d) 87
  7. 7.What is the sum of all the whole numbers from 1 to 97? (a) 4754 (b) 4656 (c) 4753 (d) 9506
  8. 8.Which term of the AP 19, 23, 27, 31, … is 87? (a) 17th (b) 19th (c) 18th (d) 20th
  9. 9.What is the missing term in the AP 9, ?, 21, 27, 33? (a) 21 (b) 14 (c) 15 (d) 16
  10. 10.What is the sum of the first 6 terms of the AP 9, 11, 13, …? (a) 84 (b) 90 (c) 19 (d) 168
  11. 11.Which term of the AP 6, 14, 22, 30, … is 246? (a) 33rd (b) 30th (c) 31st (d) 32nd
  12. 12.What is the sum of all the whole numbers from 1 to 32? (a) 1056 (b) 496 (c) 528 (d) 512
  13. 13.What is the sum of the first 12 terms of the AP 1, 7, 13, …? (a) 816 (b) 444 (c) 408 (d) 67
  14. 14.What is the missing term in the AP 2, 8, ?, 20, 26? (a) 13 (b) 20 (c) 15 (d) 14
  15. 15.What is the missing term in the AP 5, ?, 19, 26, 33? (a) 12 (b) 11 (c) 13 (d) 19
  16. 16.What is the 34th term of the AP 3, 10, 17, 24, …? (a) 238 (b) 231 (c) 241 (d) 234
  17. 17.What is the 13th term of the AP 12, 18, 24, 30, …? (a) 72 (b) 90 (c) 84 (d) 78
  18. 18.Which term of the AP 1, 5, 9, 13, … is 29? (a) 9th (b) 7th (c) 10th (d) 8th
  19. 19.What is the missing term in the AP 16, ?, 30, 37, 44? (a) 22 (b) 23 (c) 24 (d) 30
  20. 20.What is the 12th term of the AP 13, 15, 17, 19, …? (a) 24 (b) 22 (c) 35 (d) 37
  21. 21.Which term of the AP 4, 7, 10, 13, … is 121? (a) 42nd (b) 40th (c) 41st (d) 39th
  22. 22.Which term of the AP 11, 17, 23, 29, … is 191? (a) 31st (b) 30th (c) 32nd (d) 33rd
  23. 23.What is the 34th term of the AP 8, 13, 18, 23, …? (a) 165 (b) 170 (c) 173 (d) 178
  24. 24.Which term of the AP 6, 8, 10, 12, … is 36? (a) 16th (b) 17th (c) 15th (d) 18th
  25. 25.What is the sum of the first 10 terms of the AP 9, 12, 15, …? (a) 225 (b) 36 (c) 240 (d) 450
  26. 26.What is the sum of the first 10 terms of the AP 9, 11, 13, …? (a) 190 (b) 27 (c) 360 (d) 180
  27. 27.What is the 32nd term of the AP 3, 11, 19, 27, …? (a) 248 (b) 259 (c) 251 (d) 256
  28. 28.What is the sum of all the whole numbers from 1 to 15? (a) 240 (b) 120 (c) 121 (d) 105
  29. 29.What is the missing term in the AP 2, ?, 18, 26, 34? (a) 11 (b) 9 (c) 18 (d) 10
  30. 30.What is the 29th term of the AP 20, 29, 38, 47, …? (a) 252 (b) 281 (c) 261 (d) 272
  31. 31.Which term of the AP 6, 15, 24, 33, … is 186? (a) 20th (b) 23rd (c) 21st (d) 22nd
  32. 32.What is the sum of the first 28 odd numbers (1 + 3 + 5 + …)? (a) 812 (b) 55 (c) 784 (d) 406
  33. 33.What is the missing term in the AP 20, 27, ?, 41, 48? (a) 33 (b) 35 (c) 34 (d) 41
  34. 34.What is the sum of the first 8 terms of the AP 6, 11, 16, …? (a) 188 (b) 376 (c) 41 (d) 208
  35. 35.What is the 33rd term of the AP 3, 5, 7, 9, …? (a) 66 (b) 64 (c) 69 (d) 67
  36. 36.What is the sum of all the whole numbers from 1 to 54? (a) 2970 (b) 1431 (c) 1485 (d) 1458
  37. 37.What is the 13th term of the AP 18, 20, 22, 24, …? (a) 24 (b) 44 (c) 26 (d) 42
  38. 38.What is the missing term in the AP 16, 25, ?, 43, 52? (a) 43 (b) 34 (c) 33 (d) 35
  39. 39.What is the sum of the first 9 terms of the AP 1, 3, 5, …? (a) 90 (b) 162 (c) 81 (d) 17
  40. 40.What is the sum of the first 10 terms of the AP 7, 9, 11, …? (a) 320 (b) 25 (c) 170 (d) 160

Answer key

  1. 256
  2. 374
  3. 37th
  4. 162
  5. 25
  6. 100
  7. 4753
  8. 18th
  9. 15
  10. 84
  11. 31st
  12. 528
  13. 408
  14. 14
  15. 12
  16. 234
  17. 84
  18. 8th
  19. 23
  20. 35
  21. 40th
  22. 31st
  23. 173
  24. 16th
  25. 225
  26. 180
  27. 251
  28. 120
  29. 10
  30. 272
  31. 21st
  32. 784
  33. 34
  34. 188
  35. 67
  36. 1485
  37. 42
  38. 34
  39. 81
  40. 160

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