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Arithmetic Progression Worksheet for Olympiad

Maths Olympiad topic 29: Sequences and AP · Set 326 · 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 all the whole numbers from 1 to 78? (a) 3003 (b) 3042 (c) 3081 (d) 6162
  2. 2.What is the sum of the first 5 terms of the AP 6, 7, 8, …? (a) 40 (b) 10 (c) 41 (d) 80
  3. 3.What is the sum of the first 19 odd numbers (1 + 3 + 5 + …)? (a) 380 (b) 190 (c) 361 (d) 37
  4. 4.What is the sum of the first 5 terms of the AP 7, 10, 13, …? (a) 68 (b) 130 (c) 65 (d) 19
  5. 5.What is the sum of all the whole numbers from 1 to 48? (a) 2352 (b) 1128 (c) 1176 (d) 1152
  6. 6.What is the sum of the first 8 terms of the AP 1, 5, 9, …? (a) 29 (b) 120 (c) 136 (d) 240
  7. 7.What is the missing term in the AP 12, 15, ?, 21, 24? (a) 21 (b) 19 (c) 17 (d) 18
  8. 8.What is the sum of all the whole numbers from 1 to 25? (a) 326 (b) 650 (c) 325 (d) 300
  9. 9.What is the 40th term of the AP 19, 28, 37, 46, …? (a) 360 (b) 351 (c) 379 (d) 370
  10. 10.What is the missing term in the AP 6, 8, ?, 12, 14? (a) 11 (b) 10 (c) 9 (d) 12
  11. 11.What is the 23rd term of the AP 16, 19, 22, 25, …? (a) 69 (b) 66 (c) 85 (d) 82
  12. 12.What is the sum of the first 12 terms of the AP 2, 4, 6, …? (a) 24 (b) 168 (c) 156 (d) 312
  13. 13.What is the 25th term of the AP 16, 24, 32, 40, …? (a) 200 (b) 192 (c) 216 (d) 208
  14. 14.What is the sum of all the whole numbers from 1 to 60? (a) 1800 (b) 1830 (c) 3660 (d) 1770
  15. 15.What is the sum of the first 5 terms of the AP 1, 2, 3, …? (a) 16 (b) 5 (c) 15 (d) 30
  16. 16.Which term of the AP 20, 27, 34, 41, … is 132? (a) 19th (b) 17th (c) 16th (d) 18th
  17. 17.What is the sum of all the whole numbers from 1 to 55? (a) 1485 (b) 1540 (c) 3080 (d) 1541
  18. 18.What is the sum of the first 7 terms of the AP 5, 6, 7, …? (a) 112 (b) 11 (c) 57 (d) 56
  19. 19.Which term of the AP 13, 16, 19, 22, … is 109? (a) 32nd (b) 34th (c) 33rd (d) 35th
  20. 20.What is the sum of all the whole numbers from 1 to 46? (a) 2162 (b) 1058 (c) 1035 (d) 1081
  21. 21.Which term of the AP 17, 21, 25, 29, … is 97? (a) 22nd (b) 23rd (c) 20th (d) 21st
  22. 22.What is the 34th term of the AP 15, 20, 25, 30, …? (a) 185 (b) 165 (c) 180 (d) 170
  23. 23.What is the 28th term of the AP 2, 9, 16, 23, …? (a) 196 (b) 189 (c) 191 (d) 198
  24. 24.What is the sum of all the whole numbers from 1 to 77? (a) 3004 (b) 6006 (c) 2926 (d) 3003
  25. 25.What is the sum of the first 18 odd numbers (1 + 3 + 5 + …)? (a) 171 (b) 35 (c) 342 (d) 324
  26. 26.What is the 40th term of the AP 17, 23, 29, 35, …? (a) 257 (b) 240 (c) 234 (d) 251
  27. 27.What is the sum of the first 12 terms of the AP 9, 14, 19, …? (a) 64 (b) 468 (c) 438 (d) 876
  28. 28.What is the sum of the first 6 terms of the AP 5, 6, 7, …? (a) 10 (b) 90 (c) 48 (d) 45
  29. 29.What is the sum of the first 7 terms of the AP 7, 11, 15, …? (a) 266 (b) 147 (c) 133 (d) 31
  30. 30.What is the sum of the first 12 terms of the AP 6, 10, 14, …? (a) 50 (b) 360 (c) 672 (d) 336
  31. 31.What is the sum of the first 11 terms of the AP 5, 7, 9, …? (a) 165 (b) 25 (c) 176 (d) 330
  32. 32.Which term of the AP 4, 8, 12, 16, … is 68? (a) 16th (b) 17th (c) 18th (d) 19th
  33. 33.What is the sum of the first 11 terms of the AP 1, 4, 7, …? (a) 352 (b) 179 (c) 176 (d) 31
  34. 34.What is the 16th term of the AP 13, 17, 21, 25, …? (a) 60 (b) 77 (c) 73 (d) 64
  35. 35.What is the sum of the first 6 odd numbers (1 + 3 + 5 + …)? (a) 42 (b) 21 (c) 11 (d) 36
  36. 36.What is the 14th term of the AP 9, 12, 15, 18, …? (a) 51 (b) 42 (c) 39 (d) 48
  37. 37.What is the 39th term of the AP 3, 10, 17, 24, …? (a) 266 (b) 276 (c) 269 (d) 273
  38. 38.What is the missing term in the AP 20, 22, ?, 26, 28? (a) 24 (b) 26 (c) 25 (d) 23
  39. 39.What is the sum of the first 10 terms of the AP 5, 11, 17, …? (a) 59 (b) 640 (c) 350 (d) 320
  40. 40.What is the sum of the first 22 odd numbers (1 + 3 + 5 + …)? (a) 506 (b) 43 (c) 253 (d) 484

Answer key

  1. 3081
  2. 40
  3. 361
  4. 65
  5. 1176
  6. 120
  7. 18
  8. 325
  9. 370
  10. 10
  11. 82
  12. 156
  13. 208
  14. 1830
  15. 15
  16. 17th
  17. 1540
  18. 56
  19. 33rd
  20. 1081
  21. 21st
  22. 180
  23. 191
  24. 3003
  25. 324
  26. 251
  27. 438
  28. 45
  29. 133
  30. 336
  31. 165
  32. 17th
  33. 176
  34. 73
  35. 36
  36. 48
  37. 269
  38. 24
  39. 320
  40. 484

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