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Arithmetic Progression Worksheet for Olympiad

Maths Olympiad topic 29: Sequences and AP · Set 121 · 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 6 terms of the AP 10, 14, 18, …? (a) 240 (b) 30 (c) 120 (d) 132
  2. 2.What is the sum of all the whole numbers from 1 to 85? (a) 7310 (b) 3655 (c) 3656 (d) 3570
  3. 3.What is the 14th term of the AP 11, 13, 15, 17, …? (a) 37 (b) 26 (c) 28 (d) 39
  4. 4.What is the 15th term of the AP 9, 11, 13, 15, …? (a) 37 (b) 30 (c) 39 (d) 28
  5. 5.What is the sum of the first 7 terms of the AP 7, 11, 15, …? (a) 266 (b) 31 (c) 147 (d) 133
  6. 6.What is the sum of the first 8 terms of the AP 6, 10, 14, …? (a) 320 (b) 34 (c) 176 (d) 160
  7. 7.What is the sum of the first 7 odd numbers (1 + 3 + 5 + …)? (a) 28 (b) 13 (c) 56 (d) 49
  8. 8.What is the sum of the first 10 terms of the AP 1, 6, 11, …? (a) 470 (b) 46 (c) 235 (d) 260
  9. 9.What is the sum of all the whole numbers from 1 to 14? (a) 210 (b) 91 (c) 105 (d) 98
  10. 10.What is the sum of the first 27 odd numbers (1 + 3 + 5 + …)? (a) 756 (b) 378 (c) 53 (d) 729
  11. 11.What is the sum of all the whole numbers from 1 to 100? (a) 4950 (b) 5050 (c) 10100 (d) 5000
  12. 12.What is the missing term in the AP 10, ?, 16, 19, 22? (a) 16 (b) 13 (c) 12 (d) 14
  13. 13.What is the sum of all the whole numbers from 1 to 51? (a) 1275 (b) 2652 (c) 1326 (d) 1327
  14. 14.What is the 35th term of the AP 20, 25, 30, 35, …? (a) 195 (b) 190 (c) 170 (d) 175
  15. 15.What is the sum of the first 10 terms of the AP 3, 5, 7, …? (a) 120 (b) 130 (c) 240 (d) 21
  16. 16.What is the 25th term of the AP 9, 15, 21, 27, …? (a) 159 (b) 144 (c) 153 (d) 150
  17. 17.Which term of the AP 9, 17, 25, 33, … is 193? (a) 25th (b) 24th (c) 23rd (d) 26th
  18. 18.What is the 15th term of the AP 10, 14, 18, 22, …? (a) 60 (b) 70 (c) 56 (d) 66
  19. 19.What is the sum of the first 5 terms of the AP 10, 16, 22, …? (a) 34 (b) 220 (c) 125 (d) 110
  20. 20.What is the missing term in the AP 17, ?, 27, 32, 37? (a) 23 (b) 22 (c) 27 (d) 21
  21. 21.What is the sum of the first 9 odd numbers (1 + 3 + 5 + …)? (a) 81 (b) 45 (c) 17 (d) 90
  22. 22.What is the missing term in the AP 9, 16, 23, ?, 37? (a) 29 (b) 31 (c) 37 (d) 30
  23. 23.What is the 14th term of the AP 8, 10, 12, 14, …? (a) 28 (b) 26 (c) 36 (d) 34
  24. 24.What is the 28th term of the AP 13, 22, 31, 40, …? (a) 243 (b) 252 (c) 265 (d) 256
  25. 25.Which term of the AP 18, 21, 24, 27, … is 72? (a) 20th (b) 19th (c) 18th (d) 24th
  26. 26.What is the sum of the first 9 terms of the AP 7, 9, 11, …? (a) 135 (b) 270 (c) 23 (d) 144
  27. 27.What is the 30th term of the AP 7, 16, 25, 34, …? (a) 261 (b) 268 (c) 277 (d) 270
  28. 28.What is the sum of the first 24 odd numbers (1 + 3 + 5 + …)? (a) 47 (b) 576 (c) 300 (d) 600
  29. 29.What is the sum of the first 7 terms of the AP 7, 13, 19, …? (a) 175 (b) 350 (c) 43 (d) 196
  30. 30.What is the sum of the first 5 terms of the AP 2, 3, 4, …? (a) 6 (b) 40 (c) 20 (d) 21
  31. 31.What is the 34th term of the AP 16, 22, 28, 34, …? (a) 198 (b) 220 (c) 204 (d) 214
  32. 32.What is the 14th term of the AP 1, 8, 15, 22, …? (a) 91 (b) 98 (c) 92 (d) 99
  33. 33.What is the 38th term of the AP 4, 11, 18, 25, …? (a) 270 (b) 259 (c) 263 (d) 266
  34. 34.What is the sum of the first 11 terms of the AP 2, 8, 14, …? (a) 704 (b) 62 (c) 385 (d) 352
  35. 35.What is the missing term in the AP 12, 14, 16, ?, 20? (a) 17 (b) 20 (c) 18 (d) 19
  36. 36.What is the missing term in the AP 19, ?, 29, 34, 39? (a) 24 (b) 25 (c) 23 (d) 29
  37. 37.What is the 15th term of the AP 8, 11, 14, 17, …? (a) 45 (b) 53 (c) 42 (d) 50
  38. 38.What is the sum of the first 12 terms of the AP 1, 2, 3, …? (a) 156 (b) 12 (c) 84 (d) 78
  39. 39.What is the sum of the first 15 odd numbers (1 + 3 + 5 + …)? (a) 240 (b) 225 (c) 120 (d) 29
  40. 40.What is the missing term in the AP 8, 17, ?, 35, 44? (a) 35 (b) 26 (c) 25 (d) 27

Answer key

  1. 120
  2. 3655
  3. 37
  4. 37
  5. 133
  6. 160
  7. 49
  8. 235
  9. 105
  10. 729
  11. 5050
  12. 13
  13. 1326
  14. 190
  15. 120
  16. 153
  17. 24th
  18. 66
  19. 110
  20. 22
  21. 81
  22. 30
  23. 34
  24. 256
  25. 19th
  26. 135
  27. 268
  28. 576
  29. 175
  30. 20
  31. 214
  32. 92
  33. 263
  34. 352
  35. 18
  36. 24
  37. 50
  38. 78
  39. 225
  40. 26

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