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Arithmetic Progression Worksheet for Olympiad

Maths Olympiad topic 29: Sequences and AP · Set 950 · 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 1, 6, 11, …? (a) 31 (b) 112 (c) 117 (d) 224
  2. 2.What is the 25th term of the AP 15, 17, 19, 21, …? (a) 50 (b) 63 (c) 48 (d) 65
  3. 3.What is the sum of the first 28 odd numbers (1 + 3 + 5 + …)? (a) 406 (b) 784 (c) 812 (d) 55
  4. 4.What is the sum of the first 5 terms of the AP 2, 6, 10, …? (a) 100 (b) 60 (c) 18 (d) 50
  5. 5.What is the sum of the first 5 terms of the AP 10, 15, 20, …? (a) 30 (b) 100 (c) 200 (d) 105
  6. 6.What is the sum of the first 12 terms of the AP 9, 12, 15, …? (a) 324 (b) 612 (c) 306 (d) 42
  7. 7.What is the sum of the first 6 terms of the AP 8, 9, 10, …? (a) 13 (b) 63 (c) 126 (d) 66
  8. 8.What is the missing term in the AP 11, 18, ?, 32, 39? (a) 25 (b) 24 (c) 26 (d) 32
  9. 9.What is the missing term in the AP 3, 10, ?, 24, 31? (a) 16 (b) 24 (c) 17 (d) 18
  10. 10.What is the 37th term of the AP 8, 17, 26, 35, …? (a) 332 (b) 333 (c) 324 (d) 341
  11. 11.What is the sum of the first 11 terms of the AP 1, 3, 5, …? (a) 242 (b) 132 (c) 21 (d) 121
  12. 12.What is the sum of the first 5 terms of the AP 6, 7, 8, …? (a) 41 (b) 80 (c) 40 (d) 10
  13. 13.Which term of the AP 8, 16, 24, 32, … is 248? (a) 30th (b) 32nd (c) 31st (d) 33rd
  14. 14.What is the 30th term of the AP 14, 17, 20, 23, …? (a) 101 (b) 90 (c) 87 (d) 104
  15. 15.What is the sum of the first 12 terms of the AP 2, 7, 12, …? (a) 57 (b) 384 (c) 708 (d) 354
  16. 16.What is the sum of the first 8 terms of the AP 4, 5, 6, …? (a) 120 (b) 60 (c) 11 (d) 64
  17. 17.What is the 13th term of the AP 14, 19, 24, 29, …? (a) 79 (b) 60 (c) 65 (d) 74
  18. 18.What is the 37th term of the AP 13, 18, 23, 28, …? (a) 198 (b) 180 (c) 185 (d) 193
  19. 19.What is the missing term in the AP 4, 7, ?, 13, 16? (a) 10 (b) 13 (c) 11 (d) 9
  20. 20.What is the sum of all the whole numbers from 1 to 30? (a) 465 (b) 930 (c) 450 (d) 435
  21. 21.What is the sum of the first 9 terms of the AP 9, 10, 11, …? (a) 118 (b) 17 (c) 234 (d) 117
  22. 22.What is the missing term in the AP 15, ?, 23, 27, 31? (a) 18 (b) 19 (c) 20 (d) 23
  23. 23.What is the sum of the first 9 odd numbers (1 + 3 + 5 + …)? (a) 17 (b) 90 (c) 45 (d) 81
  24. 24.What is the 38th term of the AP 15, 17, 19, 21, …? (a) 74 (b) 76 (c) 91 (d) 89
  25. 25.What is the 29th term of the AP 9, 13, 17, 21, …? (a) 125 (b) 121 (c) 112 (d) 116
  26. 26.What is the missing term in the AP 20, ?, 38, 47, 56? (a) 38 (b) 28 (c) 29 (d) 30
  27. 27.What is the sum of all the whole numbers from 1 to 64? (a) 2016 (b) 4160 (c) 2048 (d) 2080
  28. 28.What is the 15th term of the AP 10, 14, 18, 22, …? (a) 66 (b) 60 (c) 70 (d) 56
  29. 29.What is the 22nd term of the AP 4, 8, 12, 16, …? (a) 84 (b) 92 (c) 88 (d) 89
  30. 30.What is the sum of the first 11 terms of the AP 1, 6, 11, …? (a) 572 (b) 51 (c) 291 (d) 286
  31. 31.What is the 19th term of the AP 7, 12, 17, 22, …? (a) 90 (b) 95 (c) 97 (d) 102
  32. 32.What is the 14th term of the AP 19, 27, 35, 43, …? (a) 104 (b) 112 (c) 131 (d) 123
  33. 33.What is the 22nd term of the AP 5, 8, 11, 14, …? (a) 66 (b) 63 (c) 68 (d) 71
  34. 34.What is the sum of the first 12 terms of the AP 1, 7, 13, …? (a) 444 (b) 816 (c) 67 (d) 408
  35. 35.What is the sum of the first 5 terms of the AP 2, 8, 14, …? (a) 140 (b) 26 (c) 70 (d) 85
  36. 36.What is the 17th term of the AP 4, 7, 10, 13, …? (a) 51 (b) 52 (c) 55 (d) 48
  37. 37.What is the sum of the first 13 odd numbers (1 + 3 + 5 + …)? (a) 25 (b) 169 (c) 182 (d) 91
  38. 38.What is the 21st term of the AP 5, 13, 21, 29, …? (a) 173 (b) 160 (c) 168 (d) 165
  39. 39.What is the sum of the first 15 odd numbers (1 + 3 + 5 + …)? (a) 120 (b) 29 (c) 225 (d) 240
  40. 40.What is the missing term in the AP 3, ?, 7, 9, 11? (a) 7 (b) 5 (c) 6 (d) 4

Answer key

  1. 112
  2. 63
  3. 784
  4. 50
  5. 100
  6. 306
  7. 63
  8. 25
  9. 17
  10. 332
  11. 121
  12. 40
  13. 31st
  14. 101
  15. 354
  16. 60
  17. 74
  18. 193
  19. 10
  20. 465
  21. 117
  22. 19
  23. 81
  24. 89
  25. 121
  26. 29
  27. 2080
  28. 66
  29. 88
  30. 286
  31. 97
  32. 123
  33. 68
  34. 408
  35. 70
  36. 52
  37. 169
  38. 165
  39. 225
  40. 5

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