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Arithmetic Progression Worksheet for Olympiad

Maths Olympiad topic 29: Sequences and AP · Set 383 · 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.Which term of the AP 6, 12, 18, 24, … is 192? (a) 34th (b) 33rd (c) 32nd (d) 31st
  2. 2.Which term of the AP 6, 8, 10, 12, … is 36? (a) 15th (b) 18th (c) 17th (d) 16th
  3. 3.What is the 24th term of the AP 17, 20, 23, 26, …? (a) 69 (b) 89 (c) 72 (d) 86
  4. 4.What is the sum of the first 6 terms of the AP 3, 5, 7, …? (a) 13 (b) 48 (c) 54 (d) 96
  5. 5.What is the sum of the first 12 terms of the AP 10, 14, 18, …? (a) 54 (b) 384 (c) 768 (d) 408
  6. 6.What is the sum of all the whole numbers from 1 to 72? (a) 2628 (b) 2556 (c) 5256 (d) 2592
  7. 7.What is the missing term in the AP 17, 25, 33, ?, 49? (a) 41 (b) 40 (c) 42 (d) 49
  8. 8.What is the sum of all the whole numbers from 1 to 26? (a) 325 (b) 351 (c) 702 (d) 338
  9. 9.What is the 19th term of the AP 1, 8, 15, 22, …? (a) 127 (b) 134 (c) 126 (d) 133
  10. 10.What is the 40th term of the AP 4, 8, 12, 16, …? (a) 160 (b) 161 (c) 156 (d) 164
  11. 11.What is the sum of the first 7 odd numbers (1 + 3 + 5 + …)? (a) 13 (b) 56 (c) 49 (d) 28
  12. 12.What is the 17th term of the AP 10, 17, 24, 31, …? (a) 129 (b) 122 (c) 112 (d) 119
  13. 13.What is the sum of the first 15 odd numbers (1 + 3 + 5 + …)? (a) 120 (b) 29 (c) 225 (d) 240
  14. 14.What is the 14th term of the AP 20, 29, 38, 47, …? (a) 137 (b) 146 (c) 117 (d) 126
  15. 15.What is the 20th term of the AP 19, 24, 29, 34, …? (a) 100 (b) 119 (c) 95 (d) 114
  16. 16.What is the sum of the first 10 terms of the AP 9, 10, 11, …? (a) 18 (b) 135 (c) 270 (d) 140
  17. 17.What is the 11th term of the AP 13, 17, 21, 25, …? (a) 44 (b) 53 (c) 57 (d) 40
  18. 18.What is the 17th term of the AP 5, 7, 9, 11, …? (a) 37 (b) 32 (c) 34 (d) 39
  19. 19.What is the sum of the first 10 terms of the AP 10, 15, 20, …? (a) 650 (b) 350 (c) 55 (d) 325
  20. 20.Which term of the AP 13, 16, 19, 22, … is 64? (a) 19th (b) 20th (c) 17th (d) 18th
  21. 21.What is the 28th term of the AP 2, 4, 6, 8, …? (a) 54 (b) 58 (c) 57 (d) 56
  22. 22.What is the 36th term of the AP 1, 7, 13, 19, …? (a) 217 (b) 211 (c) 210 (d) 216
  23. 23.What is the missing term in the AP 15, 18, 21, ?, 27? (a) 23 (b) 24 (c) 25 (d) 27
  24. 24.What is the sum of the first 11 odd numbers (1 + 3 + 5 + …)? (a) 21 (b) 132 (c) 66 (d) 121
  25. 25.What is the missing term in the AP 15, 24, ?, 42, 51? (a) 34 (b) 33 (c) 42 (d) 32
  26. 26.What is the sum of the first 6 terms of the AP 1, 5, 9, …? (a) 21 (b) 78 (c) 132 (d) 66
  27. 27.What is the 18th term of the AP 19, 23, 27, 31, …? (a) 91 (b) 72 (c) 68 (d) 87
  28. 28.What is the sum of the first 10 terms of the AP 1, 6, 11, …? (a) 470 (b) 46 (c) 235 (d) 260
  29. 29.What is the 18th term of the AP 20, 22, 24, 26, …? (a) 56 (b) 34 (c) 54 (d) 36
  30. 30.What is the sum of the first 5 odd numbers (1 + 3 + 5 + …)? (a) 9 (b) 30 (c) 15 (d) 25
  31. 31.Which term of the AP 10, 12, 14, 16, … is 46? (a) 19th (b) 20th (c) 18th (d) 23rd
  32. 32.What is the sum of the first 10 terms of the AP 1, 2, 3, …? (a) 110 (b) 60 (c) 10 (d) 55
  33. 33.What is the 13th term of the AP 13, 21, 29, 37, …? (a) 104 (b) 96 (c) 117 (d) 109
  34. 34.What is the sum of the first 5 terms of the AP 6, 7, 8, …? (a) 80 (b) 41 (c) 10 (d) 40
  35. 35.What is the sum of the first 20 odd numbers (1 + 3 + 5 + …)? (a) 210 (b) 420 (c) 400 (d) 39
  36. 36.What is the sum of the first 11 terms of the AP 4, 7, 10, …? (a) 418 (b) 34 (c) 209 (d) 212
  37. 37.What is the missing term in the AP 3, 11, ?, 27, 35? (a) 19 (b) 20 (c) 18 (d) 27
  38. 38.What is the sum of the first 11 terms of the AP 3, 9, 15, …? (a) 63 (b) 396 (c) 726 (d) 363
  39. 39.What is the sum of the first 7 terms of the AP 5, 6, 7, …? (a) 57 (b) 56 (c) 112 (d) 11
  40. 40.What is the sum of the first 12 terms of the AP 6, 8, 10, …? (a) 216 (b) 28 (c) 204 (d) 408

Answer key

  1. 32nd
  2. 16th
  3. 86
  4. 48
  5. 384
  6. 2628
  7. 41
  8. 351
  9. 127
  10. 160
  11. 49
  12. 122
  13. 225
  14. 137
  15. 114
  16. 135
  17. 53
  18. 37
  19. 325
  20. 18th
  21. 56
  22. 211
  23. 24
  24. 121
  25. 33
  26. 66
  27. 87
  28. 235
  29. 54
  30. 25
  31. 19th
  32. 55
  33. 109
  34. 40
  35. 400
  36. 209
  37. 19
  38. 363
  39. 56
  40. 204

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