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Arithmetic Progression Worksheet for Olympiad

Maths Olympiad topic 29: Sequences and AP · Set 436 · 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 the first 9 odd numbers (1 + 3 + 5 + …)? (a) 17 (b) 81 (c) 45 (d) 90
  2. 2.What is the 11th term of the AP 2, 11, 20, 29, …? (a) 99 (b) 92 (c) 90 (d) 101
  3. 3.What is the sum of the first 11 terms of the AP 4, 8, 12, …? (a) 528 (b) 264 (c) 286 (d) 44
  4. 4.What is the missing term in the AP 4, 8, ?, 16, 20? (a) 13 (b) 16 (c) 12 (d) 11
  5. 5.What is the sum of the first 5 terms of the AP 8, 12, 16, …? (a) 24 (b) 80 (c) 160 (d) 90
  6. 6.What is the 21st term of the AP 15, 17, 19, 21, …? (a) 57 (b) 40 (c) 55 (d) 42
  7. 7.What is the sum of the first 9 terms of the AP 2, 5, 8, …? (a) 126 (b) 26 (c) 252 (d) 129
  8. 8.What is the sum of the first 5 terms of the AP 9, 11, 13, …? (a) 65 (b) 70 (c) 17 (d) 130
  9. 9.What is the 11th term of the AP 5, 12, 19, 26, …? (a) 77 (b) 82 (c) 75 (d) 70
  10. 10.What is the sum of the first 10 terms of the AP 9, 12, 15, …? (a) 225 (b) 240 (c) 450 (d) 36
  11. 11.What is the sum of the first 10 terms of the AP 10, 11, 12, …? (a) 145 (b) 19 (c) 150 (d) 290
  12. 12.Which term of the AP 8, 13, 18, 23, … is 128? (a) 27th (b) 26th (c) 24th (d) 25th
  13. 13.What is the missing term in the AP 20, ?, 36, 44, 52? (a) 29 (b) 27 (c) 36 (d) 28
  14. 14.What is the missing term in the AP 11, ?, 25, 32, 39? (a) 25 (b) 17 (c) 19 (d) 18
  15. 15.What is the 16th term of the AP 17, 22, 27, 32, …? (a) 75 (b) 92 (c) 97 (d) 80
  16. 16.Which term of the AP 13, 21, 29, 37, … is 157? (a) 18th (b) 19th (c) 20th (d) 21st
  17. 17.What is the 10th term of the AP 12, 14, 16, 18, …? (a) 20 (b) 30 (c) 32 (d) 18
  18. 18.What is the 31st term of the AP 12, 21, 30, 39, …? (a) 270 (b) 282 (c) 291 (d) 279
  19. 19.What is the missing term in the AP 10, 14, 18, ?, 26? (a) 23 (b) 22 (c) 21 (d) 26
  20. 20.What is the missing term in the AP 18, 20, ?, 24, 26? (a) 21 (b) 24 (c) 23 (d) 22
  21. 21.What is the sum of the first 12 terms of the AP 10, 12, 14, …? (a) 264 (b) 252 (c) 504 (d) 32
  22. 22.What is the sum of the first 9 terms of the AP 1, 7, 13, …? (a) 49 (b) 252 (c) 450 (d) 225
  23. 23.What is the sum of the first 27 odd numbers (1 + 3 + 5 + …)? (a) 53 (b) 729 (c) 378 (d) 756
  24. 24.What is the 23rd term of the AP 4, 6, 8, 10, …? (a) 50 (b) 46 (c) 48 (d) 44
  25. 25.What is the 16th term of the AP 4, 9, 14, 19, …? (a) 80 (b) 75 (c) 84 (d) 79
  26. 26.What is the sum of all the whole numbers from 1 to 49? (a) 1176 (b) 1225 (c) 2450 (d) 1226
  27. 27.What is the 27th term of the AP 1, 5, 9, 13, …? (a) 108 (b) 105 (c) 109 (d) 104
  28. 28.Which term of the AP 10, 17, 24, 31, … is 164? (a) 24th (b) 25th (c) 22nd (d) 23rd
  29. 29.Which term of the AP 8, 15, 22, 29, … is 92? (a) 12th (b) 14th (c) 15th (d) 13th
  30. 30.What is the 35th term of the AP 9, 17, 25, 33, …? (a) 281 (b) 280 (c) 272 (d) 289
  31. 31.What is the sum of the first 12 terms of the AP 10, 11, 12, …? (a) 21 (b) 372 (c) 192 (d) 186
  32. 32.What is the missing term in the AP 7, 11, 15, ?, 23? (a) 18 (b) 23 (c) 20 (d) 19
  33. 33.What is the 13th term of the AP 8, 11, 14, 17, …? (a) 39 (b) 44 (c) 47 (d) 36
  34. 34.What is the sum of the first 10 terms of the AP 8, 12, 16, …? (a) 44 (b) 280 (c) 520 (d) 260
  35. 35.What is the sum of the first 12 terms of the AP 9, 15, 21, …? (a) 75 (b) 1008 (c) 540 (d) 504
  36. 36.What is the sum of the first 6 odd numbers (1 + 3 + 5 + …)? (a) 42 (b) 21 (c) 36 (d) 11
  37. 37.What is the sum of the first 14 odd numbers (1 + 3 + 5 + …)? (a) 27 (b) 105 (c) 210 (d) 196
  38. 38.What is the sum of all the whole numbers from 1 to 42? (a) 861 (b) 903 (c) 882 (d) 1806
  39. 39.What is the sum of the first 10 terms of the AP 2, 5, 8, …? (a) 310 (b) 170 (c) 155 (d) 29
  40. 40.What is the sum of the first 5 terms of the AP 2, 8, 14, …? (a) 70 (b) 26 (c) 85 (d) 140

Answer key

  1. 81
  2. 92
  3. 264
  4. 12
  5. 80
  6. 55
  7. 126
  8. 65
  9. 75
  10. 225
  11. 145
  12. 25th
  13. 28
  14. 18
  15. 92
  16. 19th
  17. 30
  18. 282
  19. 22
  20. 22
  21. 252
  22. 225
  23. 729
  24. 48
  25. 79
  26. 1225
  27. 105
  28. 23rd
  29. 13th
  30. 281
  31. 186
  32. 19
  33. 44
  34. 260
  35. 504
  36. 36
  37. 196
  38. 903
  39. 155
  40. 70

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