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Arithmetic Progression Worksheet for Olympiad

Maths Olympiad topic 29: Sequences and AP · Set 478 · 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 terms of the AP 6, 10, 14, …? (a) 198 (b) 216 (c) 396 (d) 38
  2. 2.What is the sum of the first 8 terms of the AP 9, 13, 17, …? (a) 368 (b) 200 (c) 184 (d) 37
  3. 3.What is the 13th term of the AP 18, 27, 36, 45, …? (a) 117 (b) 126 (c) 108 (d) 135
  4. 4.What is the 37th term of the AP 12, 14, 16, 18, …? (a) 74 (b) 72 (c) 86 (d) 84
  5. 5.Which term of the AP 2, 7, 12, 17, … is 77? (a) 16th (b) 17th (c) 15th (d) 18th
  6. 6.What is the 34th term of the AP 20, 25, 30, 35, …? (a) 190 (b) 170 (c) 165 (d) 185
  7. 7.What is the sum of the first 20 odd numbers (1 + 3 + 5 + …)? (a) 210 (b) 39 (c) 400 (d) 420
  8. 8.What is the 14th term of the AP 8, 15, 22, 29, …? (a) 98 (b) 99 (c) 106 (d) 91
  9. 9.What is the sum of the first 6 terms of the AP 9, 15, 21, …? (a) 162 (b) 144 (c) 288 (d) 39
  10. 10.What is the 23rd term of the AP 4, 12, 20, 28, …? (a) 180 (b) 176 (c) 184 (d) 188
  11. 11.What is the sum of the first 11 terms of the AP 2, 6, 10, …? (a) 42 (b) 242 (c) 264 (d) 484
  12. 12.What is the sum of all the whole numbers from 1 to 84? (a) 7140 (b) 3486 (c) 3570 (d) 3528
  13. 13.What is the missing term in the AP 20, 23, ?, 29, 32? (a) 27 (b) 29 (c) 26 (d) 25
  14. 14.What is the 13th term of the AP 18, 20, 22, 24, …? (a) 44 (b) 42 (c) 24 (d) 26
  15. 15.What is the sum of the first 5 terms of the AP 6, 7, 8, …? (a) 80 (b) 41 (c) 40 (d) 10
  16. 16.What is the missing term in the AP 3, 8, ?, 18, 23? (a) 14 (b) 18 (c) 13 (d) 12
  17. 17.What is the sum of all the whole numbers from 1 to 38? (a) 722 (b) 703 (c) 741 (d) 1482
  18. 18.What is the 14th term of the AP 8, 12, 16, 20, …? (a) 52 (b) 60 (c) 56 (d) 64
  19. 19.What is the 20th term of the AP 6, 9, 12, 15, …? (a) 60 (b) 63 (c) 57 (d) 66
  20. 20.What is the missing term in the AP 13, 21, 29, ?, 45? (a) 38 (b) 36 (c) 37 (d) 45
  21. 21.What is the 14th term of the AP 11, 19, 27, 35, …? (a) 123 (b) 112 (c) 115 (d) 104
  22. 22.What is the missing term in the AP 20, 28, 36, ?, 52? (a) 43 (b) 52 (c) 45 (d) 44
  23. 23.What is the sum of all the whole numbers from 1 to 42? (a) 1806 (b) 882 (c) 861 (d) 903
  24. 24.What is the sum of the first 9 terms of the AP 3, 6, 9, …? (a) 27 (b) 270 (c) 135 (d) 138
  25. 25.What is the 19th term of the AP 7, 13, 19, 25, …? (a) 108 (b) 115 (c) 114 (d) 121
  26. 26.Which term of the AP 15, 22, 29, 36, … is 197? (a) 26th (b) 27th (c) 28th (d) 29th
  27. 27.What is the sum of the first 12 terms of the AP 4, 5, 6, …? (a) 15 (b) 228 (c) 120 (d) 114
  28. 28.What is the missing term in the AP 1, 4, 7, ?, 13? (a) 11 (b) 13 (c) 9 (d) 10
  29. 29.What is the sum of the first 5 terms of the AP 9, 11, 13, …? (a) 65 (b) 70 (c) 17 (d) 130
  30. 30.What is the sum of all the whole numbers from 1 to 11? (a) 132 (b) 55 (c) 67 (d) 66
  31. 31.What is the missing term in the AP 18, ?, 32, 39, 46? (a) 25 (b) 26 (c) 32 (d) 24
  32. 32.What is the missing term in the AP 2, 11, ?, 29, 38? (a) 20 (b) 21 (c) 19 (d) 29
  33. 33.What is the sum of the first 8 terms of the AP 5, 10, 15, …? (a) 40 (b) 200 (c) 180 (d) 360
  34. 34.What is the 33rd term of the AP 2, 4, 6, 8, …? (a) 64 (b) 68 (c) 67 (d) 66
  35. 35.What is the missing term in the AP 8, ?, 22, 29, 36? (a) 22 (b) 16 (c) 15 (d) 14
  36. 36.What is the 29th term of the AP 16, 24, 32, 40, …? (a) 248 (b) 224 (c) 240 (d) 232
  37. 37.What is the 18th term of the AP 4, 6, 8, 10, …? (a) 36 (b) 40 (c) 38 (d) 34
  38. 38.What is the missing term in the AP 4, 12, ?, 28, 36? (a) 21 (b) 20 (c) 28 (d) 19
  39. 39.What is the sum of the first 6 terms of the AP 4, 5, 6, …? (a) 78 (b) 9 (c) 42 (d) 39
  40. 40.What is the sum of the first 8 terms of the AP 10, 13, 16, …? (a) 31 (b) 176 (c) 328 (d) 164

Answer key

  1. 198
  2. 184
  3. 126
  4. 84
  5. 16th
  6. 185
  7. 400
  8. 99
  9. 144
  10. 180
  11. 242
  12. 3570
  13. 26
  14. 42
  15. 40
  16. 13
  17. 741
  18. 60
  19. 63
  20. 37
  21. 115
  22. 44
  23. 903
  24. 135
  25. 115
  26. 27th
  27. 114
  28. 10
  29. 65
  30. 66
  31. 25
  32. 20
  33. 180
  34. 66
  35. 15
  36. 240
  37. 38
  38. 20
  39. 39
  40. 164

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