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Arithmetic Progression Worksheet for Olympiad

Maths Olympiad topic 29: Sequences and AP · Set 728 · 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 39th term of the AP 18, 27, 36, 45, …? (a) 360 (b) 369 (c) 342 (d) 351
  2. 2.What is the sum of the first 11 terms of the AP 1, 2, 3, …? (a) 67 (b) 132 (c) 66 (d) 11
  3. 3.What is the 35th term of the AP 6, 12, 18, 24, …? (a) 216 (b) 211 (c) 210 (d) 204
  4. 4.What is the 18th term of the AP 4, 8, 12, 16, …? (a) 73 (b) 76 (c) 72 (d) 68
  5. 5.What is the sum of the first 12 terms of the AP 3, 4, 5, …? (a) 204 (b) 14 (c) 102 (d) 108
  6. 6.What is the sum of the first 5 terms of the AP 2, 6, 10, …? (a) 18 (b) 100 (c) 50 (d) 60
  7. 7.What is the sum of the first 20 odd numbers (1 + 3 + 5 + …)? (a) 400 (b) 210 (c) 420 (d) 39
  8. 8.What is the sum of the first 8 terms of the AP 4, 6, 8, …? (a) 96 (b) 18 (c) 88 (d) 176
  9. 9.What is the 16th term of the AP 7, 14, 21, 28, …? (a) 113 (b) 119 (c) 105 (d) 112
  10. 10.What is the 28th term of the AP 12, 21, 30, 39, …? (a) 243 (b) 264 (c) 252 (d) 255
  11. 11.What is the missing term in the AP 11, ?, 21, 26, 31? (a) 17 (b) 21 (c) 16 (d) 15
  12. 12.Which term of the AP 10, 13, 16, 19, … is 67? (a) 19th (b) 20th (c) 21st (d) 22nd
  13. 13.What is the 33rd term of the AP 4, 10, 16, 22, …? (a) 202 (b) 192 (c) 198 (d) 196
  14. 14.What is the sum of all the whole numbers from 1 to 58? (a) 1682 (b) 1653 (c) 3422 (d) 1711
  15. 15.What is the 40th term of the AP 9, 16, 23, 30, …? (a) 289 (b) 280 (c) 282 (d) 273
  16. 16.Which term of the AP 9, 17, 25, 33, … is 153? (a) 18th (b) 21st (c) 20th (d) 19th
  17. 17.What is the sum of the first 8 terms of the AP 7, 10, 13, …? (a) 280 (b) 152 (c) 28 (d) 140
  18. 18.Which term of the AP 12, 17, 22, 27, … is 52? (a) 8th (b) 10th (c) 11th (d) 9th
  19. 19.What is the missing term in the AP 11, ?, 25, 32, 39? (a) 17 (b) 25 (c) 18 (d) 19
  20. 20.What is the sum of the first 8 terms of the AP 7, 11, 15, …? (a) 336 (b) 184 (c) 168 (d) 35
  21. 21.What is the missing term in the AP 8, 14, 20, ?, 32? (a) 25 (b) 26 (c) 32 (d) 27
  22. 22.What is the sum of all the whole numbers from 1 to 66? (a) 2211 (b) 2145 (c) 2178 (d) 4422
  23. 23.What is the missing term in the AP 12, 21, 30, ?, 48? (a) 39 (b) 48 (c) 38 (d) 40
  24. 24.What is the missing term in the AP 13, 18, ?, 28, 33? (a) 22 (b) 24 (c) 28 (d) 23
  25. 25.What is the 39th term of the AP 5, 13, 21, 29, …? (a) 304 (b) 309 (c) 312 (d) 317
  26. 26.What is the missing term in the AP 7, 11, 15, ?, 23? (a) 23 (b) 19 (c) 20 (d) 18
  27. 27.What is the missing term in the AP 11, 16, ?, 26, 31? (a) 20 (b) 22 (c) 21 (d) 26
  28. 28.What is the 23rd term of the AP 7, 12, 17, 22, …? (a) 117 (b) 110 (c) 122 (d) 115
  29. 29.What is the sum of all the whole numbers from 1 to 34? (a) 578 (b) 1190 (c) 595 (d) 561
  30. 30.What is the 26th term of the AP 10, 18, 26, 34, …? (a) 218 (b) 208 (c) 200 (d) 210
  31. 31.Which term of the AP 5, 12, 19, 26, … is 68? (a) 9th (b) 11th (c) 12th (d) 10th
  32. 32.What is the sum of all the whole numbers from 1 to 55? (a) 1485 (b) 1541 (c) 3080 (d) 1540
  33. 33.Which term of the AP 8, 17, 26, 35, … is 179? (a) 21st (b) 19th (c) 20th (d) 22nd
  34. 34.What is the sum of the first 11 terms of the AP 2, 3, 4, …? (a) 154 (b) 12 (c) 77 (d) 78
  35. 35.What is the sum of the first 6 terms of the AP 9, 13, 17, …? (a) 114 (b) 29 (c) 126 (d) 228
  36. 36.What is the sum of all the whole numbers from 1 to 69? (a) 2346 (b) 4830 (c) 2415 (d) 2416
  37. 37.What is the sum of the first 5 terms of the AP 7, 11, 15, …? (a) 150 (b) 75 (c) 23 (d) 85
  38. 38.What is the 21st term of the AP 13, 22, 31, 40, …? (a) 180 (b) 202 (c) 193 (d) 189
  39. 39.What is the sum of all the whole numbers from 1 to 74? (a) 2738 (b) 5550 (c) 2701 (d) 2775
  40. 40.What is the sum of the first 5 terms of the AP 3, 8, 13, …? (a) 130 (b) 23 (c) 65 (d) 70

Answer key

  1. 360
  2. 66
  3. 210
  4. 72
  5. 102
  6. 50
  7. 400
  8. 88
  9. 112
  10. 255
  11. 16
  12. 20th
  13. 196
  14. 1711
  15. 282
  16. 19th
  17. 140
  18. 9th
  19. 18
  20. 168
  21. 26
  22. 2211
  23. 39
  24. 23
  25. 309
  26. 19
  27. 21
  28. 117
  29. 595
  30. 210
  31. 10th
  32. 1540
  33. 20th
  34. 77
  35. 114
  36. 2415
  37. 75
  38. 193
  39. 2775
  40. 65

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