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Arithmetic Progression Worksheet for Olympiad

Maths Olympiad topic 29: Sequences and AP · Set 466 · 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 8, 11, 14, …? (a) 119 (b) 238 (c) 122 (d) 26
  2. 2.What is the missing term in the AP 8, 14, 20, ?, 32? (a) 25 (b) 32 (c) 27 (d) 26
  3. 3.What is the sum of the first 8 terms of the AP 3, 8, 13, …? (a) 38 (b) 164 (c) 184 (d) 328
  4. 4.Which term of the AP 15, 18, 21, 24, … is 60? (a) 17th (b) 15th (c) 20th (d) 16th
  5. 5.What is the sum of the first 11 terms of the AP 5, 6, 7, …? (a) 111 (b) 220 (c) 110 (d) 15
  6. 6.What is the sum of the first 9 odd numbers (1 + 3 + 5 + …)? (a) 45 (b) 90 (c) 17 (d) 81
  7. 7.What is the sum of all the whole numbers from 1 to 99? (a) 4950 (b) 4851 (c) 4951 (d) 9900
  8. 8.What is the sum of the first 24 odd numbers (1 + 3 + 5 + …)? (a) 47 (b) 600 (c) 300 (d) 576
  9. 9.What is the 18th term of the AP 12, 15, 18, 21, …? (a) 63 (b) 54 (c) 51 (d) 66
  10. 10.What is the sum of the first 6 terms of the AP 7, 9, 11, …? (a) 78 (b) 144 (c) 17 (d) 72
  11. 11.What is the sum of the first 6 terms of the AP 3, 4, 5, …? (a) 8 (b) 66 (c) 33 (d) 36
  12. 12.What is the 30th term of the AP 20, 23, 26, 29, …? (a) 107 (b) 87 (c) 110 (d) 90
  13. 13.What is the missing term in the AP 11, 19, 27, ?, 43? (a) 34 (b) 35 (c) 36 (d) 43
  14. 14.What is the 34th term of the AP 11, 20, 29, 38, …? (a) 317 (b) 297 (c) 308 (d) 306
  15. 15.What is the sum of the first 10 terms of the AP 10, 15, 20, …? (a) 325 (b) 350 (c) 650 (d) 55
  16. 16.What is the missing term in the AP 2, 8, 14, ?, 26? (a) 20 (b) 19 (c) 26 (d) 21
  17. 17.What is the missing term in the AP 13, 15, 17, ?, 21? (a) 20 (b) 19 (c) 21 (d) 18
  18. 18.What is the 37th term of the AP 10, 12, 14, 16, …? (a) 82 (b) 72 (c) 84 (d) 74
  19. 19.What is the 29th term of the AP 15, 17, 19, 21, …? (a) 58 (b) 71 (c) 73 (d) 56
  20. 20.What is the missing term in the AP 9, 17, 25, ?, 41? (a) 41 (b) 34 (c) 33 (d) 32
  21. 21.What is the sum of all the whole numbers from 1 to 33? (a) 562 (b) 528 (c) 561 (d) 1122
  22. 22.What is the 16th term of the AP 16, 21, 26, 31, …? (a) 96 (b) 75 (c) 80 (d) 91
  23. 23.What is the sum of the first 21 odd numbers (1 + 3 + 5 + …)? (a) 231 (b) 441 (c) 41 (d) 462
  24. 24.What is the missing term in the AP 10, 13, 16, ?, 22? (a) 22 (b) 19 (c) 20 (d) 18
  25. 25.What is the 25th term of the AP 16, 21, 26, 31, …? (a) 136 (b) 141 (c) 120 (d) 125
  26. 26.Which term of the AP 6, 15, 24, 33, … is 267? (a) 30th (b) 29th (c) 32nd (d) 31st
  27. 27.What is the missing term in the AP 4, 6, 8, ?, 12? (a) 10 (b) 11 (c) 12 (d) 9
  28. 28.What is the sum of the first 8 terms of the AP 2, 4, 6, …? (a) 16 (b) 72 (c) 80 (d) 144
  29. 29.What is the 38th term of the AP 19, 22, 25, 28, …? (a) 130 (b) 111 (c) 114 (d) 133
  30. 30.What is the missing term in the AP 2, 7, ?, 17, 22? (a) 17 (b) 13 (c) 11 (d) 12
  31. 31.What is the sum of all the whole numbers from 1 to 44? (a) 1980 (b) 968 (c) 990 (d) 946
  32. 32.What is the missing term in the AP 20, 27, 34, ?, 48? (a) 40 (b) 48 (c) 42 (d) 41
  33. 33.What is the sum of the first 6 terms of the AP 6, 7, 8, …? (a) 54 (b) 11 (c) 51 (d) 102
  34. 34.What is the sum of the first 8 terms of the AP 4, 8, 12, …? (a) 160 (b) 288 (c) 144 (d) 32
  35. 35.What is the sum of the first 30 odd numbers (1 + 3 + 5 + …)? (a) 59 (b) 930 (c) 900 (d) 465
  36. 36.What is the missing term in the AP 7, 9, 11, ?, 15? (a) 13 (b) 15 (c) 12 (d) 14
  37. 37.What is the 22nd term of the AP 12, 15, 18, 21, …? (a) 78 (b) 66 (c) 63 (d) 75
  38. 38.What is the 38th term of the AP 12, 14, 16, 18, …? (a) 88 (b) 86 (c) 74 (d) 76
  39. 39.What is the 12th term of the AP 13, 15, 17, 19, …? (a) 22 (b) 24 (c) 35 (d) 37
  40. 40.What is the sum of the first 6 terms of the AP 6, 10, 14, …? (a) 96 (b) 108 (c) 26 (d) 192

Answer key

  1. 119
  2. 26
  3. 164
  4. 16th
  5. 110
  6. 81
  7. 4950
  8. 576
  9. 63
  10. 72
  11. 33
  12. 107
  13. 35
  14. 308
  15. 325
  16. 20
  17. 19
  18. 82
  19. 71
  20. 33
  21. 561
  22. 91
  23. 441
  24. 19
  25. 136
  26. 30th
  27. 10
  28. 72
  29. 130
  30. 12
  31. 990
  32. 41
  33. 51
  34. 144
  35. 900
  36. 13
  37. 75
  38. 86
  39. 35
  40. 96

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