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Arithmetic Progression Worksheet for Olympiad

Maths Olympiad topic 29: Sequences and AP · Set 163 · 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 26th term of the AP 6, 12, 18, 24, …? (a) 157 (b) 156 (c) 162 (d) 150
  2. 2.What is the 40th term of the AP 20, 24, 28, 32, …? (a) 180 (b) 176 (c) 156 (d) 160
  3. 3.What is the sum of the first 29 odd numbers (1 + 3 + 5 + …)? (a) 435 (b) 57 (c) 870 (d) 841
  4. 4.What is the sum of the first 5 terms of the AP 8, 12, 16, …? (a) 90 (b) 24 (c) 80 (d) 160
  5. 5.What is the 28th term of the AP 6, 13, 20, 27, …? (a) 195 (b) 196 (c) 189 (d) 202
  6. 6.What is the sum of all the whole numbers from 1 to 84? (a) 3528 (b) 7140 (c) 3570 (d) 3486
  7. 7.Which term of the AP 15, 24, 33, 42, … is 294? (a) 34th (b) 32nd (c) 33rd (d) 31st
  8. 8.Which term of the AP 4, 12, 20, 28, … is 92? (a) 11th (b) 12th (c) 13th (d) 14th
  9. 9.What is the 13th term of the AP 6, 13, 20, 27, …? (a) 97 (b) 84 (c) 90 (d) 91
  10. 10.What is the sum of the first 11 terms of the AP 2, 8, 14, …? (a) 352 (b) 62 (c) 385 (d) 704
  11. 11.Which term of the AP 13, 21, 29, 37, … is 109? (a) 13th (b) 12th (c) 15th (d) 14th
  12. 12.What is the 38th term of the AP 13, 16, 19, 22, …? (a) 124 (b) 114 (c) 111 (d) 127
  13. 13.What is the sum of the first 9 terms of the AP 6, 11, 16, …? (a) 468 (b) 46 (c) 234 (d) 239
  14. 14.What is the 13th term of the AP 9, 16, 23, 30, …? (a) 84 (b) 91 (c) 93 (d) 100
  15. 15.What is the 19th term of the AP 14, 20, 26, 32, …? (a) 122 (b) 108 (c) 128 (d) 114
  16. 16.What is the 25th term of the AP 18, 27, 36, 45, …? (a) 216 (b) 243 (c) 225 (d) 234
  17. 17.What is the sum of the first 10 terms of the AP 10, 14, 18, …? (a) 300 (b) 46 (c) 560 (d) 280
  18. 18.What is the 37th term of the AP 20, 22, 24, 26, …? (a) 72 (b) 74 (c) 94 (d) 92
  19. 19.Which term of the AP 16, 19, 22, 25, … is 85? (a) 23rd (b) 25th (c) 24th (d) 26th
  20. 20.What is the 33rd term of the AP 17, 22, 27, 32, …? (a) 160 (b) 182 (c) 165 (d) 177
  21. 21.What is the sum of all the whole numbers from 1 to 82? (a) 3403 (b) 3362 (c) 6806 (d) 3321
  22. 22.What is the sum of the first 12 terms of the AP 3, 7, 11, …? (a) 47 (b) 600 (c) 300 (d) 324
  23. 23.What is the 39th term of the AP 6, 8, 10, 12, …? (a) 84 (b) 78 (c) 82 (d) 76
  24. 24.What is the 14th term of the AP 12, 20, 28, 36, …? (a) 104 (b) 112 (c) 124 (d) 116
  25. 25.What is the missing term in the AP 18, ?, 26, 30, 34? (a) 21 (b) 23 (c) 26 (d) 22
  26. 26.What is the sum of the first 9 terms of the AP 1, 4, 7, …? (a) 25 (b) 120 (c) 117 (d) 234
  27. 27.What is the missing term in the AP 15, 20, ?, 30, 35? (a) 25 (b) 30 (c) 26 (d) 24
  28. 28.What is the sum of all the whole numbers from 1 to 27? (a) 378 (b) 351 (c) 756 (d) 379
  29. 29.What is the sum of the first 18 odd numbers (1 + 3 + 5 + …)? (a) 342 (b) 35 (c) 324 (d) 171
  30. 30.What is the sum of the first 24 odd numbers (1 + 3 + 5 + …)? (a) 576 (b) 600 (c) 300 (d) 47
  31. 31.What is the sum of the first 6 terms of the AP 1, 7, 13, …? (a) 31 (b) 192 (c) 114 (d) 96
  32. 32.What is the sum of the first 8 terms of the AP 8, 11, 14, …? (a) 160 (b) 296 (c) 148 (d) 29
  33. 33.What is the missing term in the AP 8, ?, 24, 32, 40? (a) 24 (b) 15 (c) 16 (d) 17
  34. 34.What is the 23rd term of the AP 7, 9, 11, 13, …? (a) 53 (b) 51 (c) 46 (d) 44
  35. 35.What is the sum of the first 6 terms of the AP 2, 4, 6, …? (a) 84 (b) 48 (c) 42 (d) 12
  36. 36.What is the sum of all the whole numbers from 1 to 78? (a) 3081 (b) 3042 (c) 3003 (d) 6162
  37. 37.What is the sum of all the whole numbers from 1 to 30? (a) 435 (b) 930 (c) 465 (d) 450
  38. 38.What is the sum of the first 12 terms of the AP 4, 9, 14, …? (a) 59 (b) 378 (c) 408 (d) 756
  39. 39.Which term of the AP 20, 24, 28, 32, … is 80? (a) 20th (b) 15th (c) 17th (d) 16th
  40. 40.What is the 23rd term of the AP 9, 15, 21, 27, …? (a) 141 (b) 138 (c) 147 (d) 132

Answer key

  1. 156
  2. 176
  3. 841
  4. 80
  5. 195
  6. 3570
  7. 32nd
  8. 12th
  9. 90
  10. 352
  11. 13th
  12. 124
  13. 234
  14. 93
  15. 122
  16. 234
  17. 280
  18. 92
  19. 24th
  20. 177
  21. 3403
  22. 300
  23. 82
  24. 116
  25. 22
  26. 117
  27. 25
  28. 378
  29. 324
  30. 576
  31. 96
  32. 148
  33. 16
  34. 51
  35. 42
  36. 3081
  37. 465
  38. 378
  39. 16th
  40. 141

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