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Arithmetic Progression Worksheet for Olympiad

Maths Olympiad topic 29: Sequences and AP · Set 753 · 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 19th term of the AP 11, 19, 27, 35, …? (a) 163 (b) 155 (c) 152 (d) 144
  2. 2.What is the sum of the first 9 odd numbers (1 + 3 + 5 + …)? (a) 17 (b) 81 (c) 90 (d) 45
  3. 3.What is the sum of the first 6 terms of the AP 5, 6, 7, …? (a) 48 (b) 10 (c) 90 (d) 45
  4. 4.What is the sum of the first 12 odd numbers (1 + 3 + 5 + …)? (a) 78 (b) 156 (c) 144 (d) 23
  5. 5.What is the 15th term of the AP 12, 20, 28, 36, …? (a) 132 (b) 124 (c) 120 (d) 112
  6. 6.What is the 18th term of the AP 1, 8, 15, 22, …? (a) 119 (b) 120 (c) 126 (d) 127
  7. 7.What is the 22nd term of the AP 11, 15, 19, 23, …? (a) 88 (b) 84 (c) 99 (d) 95
  8. 8.What is the sum of the first 7 odd numbers (1 + 3 + 5 + …)? (a) 28 (b) 56 (c) 13 (d) 49
  9. 9.What is the sum of the first 8 terms of the AP 4, 8, 12, …? (a) 144 (b) 160 (c) 32 (d) 288
  10. 10.Which term of the AP 6, 9, 12, 15, … is 36? (a) 13th (b) 11th (c) 12th (d) 10th
  11. 11.What is the sum of the first 10 terms of the AP 2, 4, 6, …? (a) 120 (b) 20 (c) 110 (d) 220
  12. 12.What is the 15th term of the AP 1, 6, 11, 16, …? (a) 76 (b) 75 (c) 71 (d) 70
  13. 13.What is the sum of the first 9 terms of the AP 1, 4, 7, …? (a) 117 (b) 25 (c) 234 (d) 120
  14. 14.What is the sum of the first 21 odd numbers (1 + 3 + 5 + …)? (a) 41 (b) 231 (c) 462 (d) 441
  15. 15.What is the 29th term of the AP 2, 11, 20, 29, …? (a) 261 (b) 252 (c) 254 (d) 263
  16. 16.What is the 21st term of the AP 1, 3, 5, 7, …? (a) 40 (b) 42 (c) 43 (d) 41
  17. 17.What is the 18th term of the AP 9, 12, 15, 18, …? (a) 54 (b) 63 (c) 51 (d) 60
  18. 18.What is the 31st term of the AP 18, 22, 26, 30, …? (a) 124 (b) 142 (c) 120 (d) 138
  19. 19.What is the 16th term of the AP 7, 13, 19, 25, …? (a) 97 (b) 103 (c) 96 (d) 90
  20. 20.What is the sum of the first 10 terms of the AP 6, 8, 10, …? (a) 24 (b) 150 (c) 160 (d) 300
  21. 21.What is the missing term in the AP 17, 24, ?, 38, 45? (a) 30 (b) 31 (c) 32 (d) 38
  22. 22.What is the 35th term of the AP 1, 7, 13, 19, …? (a) 211 (b) 205 (c) 210 (d) 204
  23. 23.What is the 39th term of the AP 6, 15, 24, 33, …? (a) 342 (b) 357 (c) 351 (d) 348
  24. 24.What is the 13th term of the AP 1, 10, 19, 28, …? (a) 118 (b) 108 (c) 117 (d) 109
  25. 25.What is the sum of the first 12 terms of the AP 9, 15, 21, …? (a) 75 (b) 1008 (c) 540 (d) 504
  26. 26.What is the 14th term of the AP 5, 10, 15, 20, …? (a) 65 (b) 75 (c) 71 (d) 70
  27. 27.What is the 20th term of the AP 16, 24, 32, 40, …? (a) 160 (b) 168 (c) 176 (d) 152
  28. 28.What is the missing term in the AP 5, ?, 23, 32, 41? (a) 13 (b) 14 (c) 23 (d) 15
  29. 29.Which term of the AP 12, 21, 30, 39, … is 138? (a) 14th (b) 17th (c) 15th (d) 16th
  30. 30.What is the 39th term of the AP 14, 22, 30, 38, …? (a) 312 (b) 318 (c) 326 (d) 304
  31. 31.Which term of the AP 16, 20, 24, 28, … is 96? (a) 21st (b) 24th (c) 22nd (d) 20th
  32. 32.Which term of the AP 14, 19, 24, 29, … is 179? (a) 33rd (b) 35th (c) 34th (d) 36th
  33. 33.What is the 38th term of the AP 19, 27, 35, 43, …? (a) 296 (b) 323 (c) 304 (d) 315
  34. 34.What is the sum of all the whole numbers from 1 to 15? (a) 105 (b) 240 (c) 120 (d) 121
  35. 35.What is the sum of the first 13 odd numbers (1 + 3 + 5 + …)? (a) 169 (b) 25 (c) 91 (d) 182
  36. 36.What is the sum of the first 11 terms of the AP 6, 7, 8, …? (a) 16 (b) 122 (c) 242 (d) 121
  37. 37.What is the sum of the first 9 terms of the AP 9, 13, 17, …? (a) 225 (b) 243 (c) 41 (d) 450
  38. 38.What is the 25th term of the AP 2, 8, 14, 20, …? (a) 144 (b) 152 (c) 146 (d) 150
  39. 39.What is the sum of the first 12 terms of the AP 5, 10, 15, …? (a) 60 (b) 390 (c) 420 (d) 780
  40. 40.What is the 11th term of the AP 9, 15, 21, 27, …? (a) 75 (b) 69 (c) 60 (d) 66

Answer key

  1. 155
  2. 81
  3. 45
  4. 144
  5. 124
  6. 120
  7. 95
  8. 49
  9. 144
  10. 11th
  11. 110
  12. 71
  13. 117
  14. 441
  15. 254
  16. 41
  17. 60
  18. 138
  19. 97
  20. 150
  21. 31
  22. 205
  23. 348
  24. 109
  25. 504
  26. 70
  27. 168
  28. 14
  29. 15th
  30. 318
  31. 21st
  32. 34th
  33. 315
  34. 120
  35. 169
  36. 121
  37. 225
  38. 146
  39. 390
  40. 69

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