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Arithmetic Progression Worksheet for Olympiad

Maths Olympiad topic 29: Sequences and AP · Set 468 · 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 7 terms of the AP 10, 16, 22, …? (a) 217 (b) 392 (c) 196 (d) 46
  2. 2.What is the 32nd term of the AP 4, 13, 22, 31, …? (a) 288 (b) 292 (c) 283 (d) 279
  3. 3.What is the missing term in the AP 3, 9, 15, ?, 27? (a) 21 (b) 20 (c) 22 (d) 27
  4. 4.What is the 38th term of the AP 13, 15, 17, 19, …? (a) 87 (b) 76 (c) 89 (d) 74
  5. 5.What is the missing term in the AP 14, ?, 30, 38, 46? (a) 21 (b) 30 (c) 23 (d) 22
  6. 6.What is the sum of the first 10 terms of the AP 6, 9, 12, …? (a) 33 (b) 195 (c) 390 (d) 210
  7. 7.What is the sum of the first 12 terms of the AP 5, 7, 9, …? (a) 27 (b) 204 (c) 192 (d) 384
  8. 8.What is the sum of the first 15 odd numbers (1 + 3 + 5 + …)? (a) 120 (b) 240 (c) 29 (d) 225
  9. 9.What is the missing term in the AP 17, 20, 23, ?, 29? (a) 25 (b) 29 (c) 27 (d) 26
  10. 10.What is the missing term in the AP 3, 6, 9, ?, 15? (a) 15 (b) 13 (c) 11 (d) 12
  11. 11.What is the sum of the first 10 terms of the AP 4, 9, 14, …? (a) 290 (b) 49 (c) 530 (d) 265
  12. 12.What is the sum of the first 9 terms of the AP 1, 7, 13, …? (a) 450 (b) 225 (c) 49 (d) 252
  13. 13.What is the sum of all the whole numbers from 1 to 80? (a) 3240 (b) 6480 (c) 3160 (d) 3200
  14. 14.What is the sum of the first 30 odd numbers (1 + 3 + 5 + …)? (a) 59 (b) 930 (c) 900 (d) 465
  15. 15.What is the missing term in the AP 19, ?, 29, 34, 39? (a) 29 (b) 23 (c) 24 (d) 25
  16. 16.What is the 16th term of the AP 20, 23, 26, 29, …? (a) 48 (b) 68 (c) 65 (d) 45
  17. 17.What is the missing term in the AP 2, 8, ?, 20, 26? (a) 13 (b) 20 (c) 15 (d) 14
  18. 18.What is the sum of all the whole numbers from 1 to 71? (a) 5112 (b) 2557 (c) 2485 (d) 2556
  19. 19.What is the sum of the first 9 odd numbers (1 + 3 + 5 + …)? (a) 90 (b) 81 (c) 17 (d) 45
  20. 20.What is the missing term in the AP 17, ?, 27, 32, 37? (a) 22 (b) 23 (c) 27 (d) 21
  21. 21.What is the 15th term of the AP 1, 7, 13, 19, …? (a) 91 (b) 84 (c) 90 (d) 85
  22. 22.What is the 32nd term of the AP 5, 10, 15, 20, …? (a) 160 (b) 161 (c) 155 (d) 165
  23. 23.What is the 34th term of the AP 19, 22, 25, 28, …? (a) 121 (b) 102 (c) 118 (d) 99
  24. 24.What is the sum of the first 10 odd numbers (1 + 3 + 5 + …)? (a) 19 (b) 110 (c) 100 (d) 55
  25. 25.What is the missing term in the AP 6, 9, 12, ?, 18? (a) 16 (b) 15 (c) 14 (d) 18
  26. 26.What is the 13th term of the AP 13, 19, 25, 31, …? (a) 72 (b) 91 (c) 85 (d) 78
  27. 27.What is the sum of the first 10 terms of the AP 2, 7, 12, …? (a) 245 (b) 270 (c) 490 (d) 47
  28. 28.What is the 31st term of the AP 18, 20, 22, 24, …? (a) 80 (b) 62 (c) 60 (d) 78
  29. 29.What is the missing term in the AP 1, 3, ?, 7, 9? (a) 5 (b) 6 (c) 4 (d) 7
  30. 30.What is the sum of all the whole numbers from 1 to 13? (a) 78 (b) 182 (c) 91 (d) 92
  31. 31.What is the missing term in the AP 3, ?, 13, 18, 23? (a) 7 (b) 9 (c) 13 (d) 8
  32. 32.What is the sum of all the whole numbers from 1 to 41? (a) 1722 (b) 862 (c) 861 (d) 820
  33. 33.Which term of the AP 5, 8, 11, 14, … is 41? (a) 13th (b) 14th (c) 15th (d) 12th
  34. 34.What is the 13th term of the AP 1, 6, 11, 16, …? (a) 60 (b) 61 (c) 65 (d) 66
  35. 35.What is the 24th term of the AP 20, 25, 30, 35, …? (a) 140 (b) 135 (c) 115 (d) 120
  36. 36.What is the sum of the first 11 terms of the AP 9, 11, 13, …? (a) 209 (b) 418 (c) 29 (d) 220
  37. 37.What is the sum of the first 12 terms of the AP 7, 13, 19, …? (a) 480 (b) 960 (c) 73 (d) 516
  38. 38.What is the sum of the first 6 terms of the AP 7, 10, 13, …? (a) 87 (b) 174 (c) 96 (d) 22
  39. 39.What is the sum of the first 11 terms of the AP 8, 11, 14, …? (a) 256 (b) 253 (c) 506 (d) 38
  40. 40.What is the missing term in the AP 17, 25, 33, ?, 49? (a) 42 (b) 41 (c) 40 (d) 49

Answer key

  1. 196
  2. 283
  3. 21
  4. 87
  5. 22
  6. 195
  7. 192
  8. 225
  9. 26
  10. 12
  11. 265
  12. 225
  13. 3240
  14. 900
  15. 24
  16. 65
  17. 14
  18. 2556
  19. 81
  20. 22
  21. 85
  22. 160
  23. 118
  24. 100
  25. 15
  26. 85
  27. 245
  28. 78
  29. 5
  30. 91
  31. 8
  32. 861
  33. 13th
  34. 61
  35. 135
  36. 209
  37. 480
  38. 87
  39. 253
  40. 41

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