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Arithmetic Progression Worksheet for Olympiad

Maths Olympiad topic 29: Sequences and AP · Set 570 · 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 13th term of the AP 8, 17, 26, 35, …? (a) 125 (b) 108 (c) 116 (d) 117
  2. 2.What is the sum of the first 9 terms of the AP 3, 9, 15, …? (a) 486 (b) 243 (c) 270 (d) 51
  3. 3.What is the 29th term of the AP 14, 17, 20, 23, …? (a) 84 (b) 101 (c) 98 (d) 87
  4. 4.What is the sum of the first 12 terms of the AP 1, 3, 5, …? (a) 288 (b) 23 (c) 144 (d) 156
  5. 5.What is the 24th term of the AP 8, 10, 12, 14, …? (a) 54 (b) 46 (c) 56 (d) 48
  6. 6.What is the 34th term of the AP 8, 16, 24, 32, …? (a) 273 (b) 264 (c) 280 (d) 272
  7. 7.What is the missing term in the AP 5, 8, 11, ?, 17? (a) 13 (b) 15 (c) 17 (d) 14
  8. 8.What is the sum of the first 8 terms of the AP 10, 13, 16, …? (a) 164 (b) 31 (c) 328 (d) 176
  9. 9.What is the 28th term of the AP 2, 9, 16, 23, …? (a) 198 (b) 189 (c) 196 (d) 191
  10. 10.What is the 29th term of the AP 7, 9, 11, 13, …? (a) 63 (b) 65 (c) 58 (d) 56
  11. 11.Which term of the AP 10, 15, 20, 25, … is 125? (a) 26th (b) 25th (c) 23rd (d) 24th
  12. 12.What is the sum of all the whole numbers from 1 to 34? (a) 578 (b) 1190 (c) 595 (d) 561
  13. 13.What is the 16th term of the AP 17, 20, 23, 26, …? (a) 65 (b) 62 (c) 48 (d) 45
  14. 14.What is the sum of all the whole numbers from 1 to 18? (a) 342 (b) 171 (c) 162 (d) 153
  15. 15.What is the missing term in the AP 5, ?, 19, 26, 33? (a) 13 (b) 19 (c) 11 (d) 12
  16. 16.What is the sum of all the whole numbers from 1 to 19? (a) 191 (b) 380 (c) 171 (d) 190
  17. 17.What is the missing term in the AP 10, 12, ?, 16, 18? (a) 13 (b) 15 (c) 14 (d) 16
  18. 18.What is the 26th term of the AP 20, 26, 32, 38, …? (a) 150 (b) 170 (c) 176 (d) 156
  19. 19.What is the sum of the first 9 terms of the AP 9, 15, 21, …? (a) 57 (b) 594 (c) 324 (d) 297
  20. 20.What is the sum of the first 10 terms of the AP 9, 10, 11, …? (a) 270 (b) 18 (c) 140 (d) 135
  21. 21.What is the missing term in the AP 16, 19, 22, ?, 28? (a) 24 (b) 26 (c) 28 (d) 25
  22. 22.What is the sum of the first 6 terms of the AP 7, 8, 9, …? (a) 114 (b) 57 (c) 12 (d) 60
  23. 23.What is the 35th term of the AP 20, 29, 38, 47, …? (a) 335 (b) 306 (c) 315 (d) 326
  24. 24.What is the missing term in the AP 6, 13, ?, 27, 34? (a) 19 (b) 20 (c) 21 (d) 27
  25. 25.What is the sum of all the whole numbers from 1 to 59? (a) 1711 (b) 1771 (c) 1770 (d) 3540
  26. 26.What is the sum of all the whole numbers from 1 to 22? (a) 231 (b) 506 (c) 242 (d) 253
  27. 27.What is the sum of the first 27 odd numbers (1 + 3 + 5 + …)? (a) 756 (b) 53 (c) 729 (d) 378
  28. 28.What is the sum of the first 10 odd numbers (1 + 3 + 5 + …)? (a) 100 (b) 19 (c) 55 (d) 110
  29. 29.Which term of the AP 8, 14, 20, 26, … is 92? (a) 17th (b) 14th (c) 15th (d) 16th
  30. 30.What is the sum of all the whole numbers from 1 to 25? (a) 325 (b) 300 (c) 326 (d) 650
  31. 31.Which term of the AP 16, 18, 20, 22, … is 54? (a) 27th (b) 20th (c) 21st (d) 19th
  32. 32.What is the sum of all the whole numbers from 1 to 40? (a) 820 (b) 780 (c) 800 (d) 1640
  33. 33.What is the 38th term of the AP 10, 19, 28, 37, …? (a) 342 (b) 343 (c) 333 (d) 352
  34. 34.What is the sum of the first 5 terms of the AP 3, 6, 9, …? (a) 90 (b) 48 (c) 15 (d) 45
  35. 35.What is the sum of all the whole numbers from 1 to 24? (a) 600 (b) 288 (c) 276 (d) 300
  36. 36.What is the sum of the first 7 terms of the AP 2, 3, 4, …? (a) 70 (b) 35 (c) 8 (d) 36
  37. 37.What is the sum of the first 5 terms of the AP 10, 16, 22, …? (a) 125 (b) 34 (c) 220 (d) 110
  38. 38.What is the sum of all the whole numbers from 1 to 43? (a) 947 (b) 903 (c) 946 (d) 1892
  39. 39.What is the missing term in the AP 20, ?, 30, 35, 40? (a) 25 (b) 24 (c) 30 (d) 26
  40. 40.What is the missing term in the AP 10, 14, ?, 22, 26? (a) 18 (b) 19 (c) 17 (d) 22

Answer key

  1. 116
  2. 243
  3. 98
  4. 144
  5. 54
  6. 272
  7. 14
  8. 164
  9. 191
  10. 63
  11. 24th
  12. 595
  13. 62
  14. 171
  15. 12
  16. 190
  17. 14
  18. 170
  19. 297
  20. 135
  21. 25
  22. 57
  23. 326
  24. 20
  25. 1770
  26. 253
  27. 729
  28. 100
  29. 15th
  30. 325
  31. 20th
  32. 820
  33. 343
  34. 45
  35. 300
  36. 35
  37. 110
  38. 946
  39. 25
  40. 18

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