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Arithmetic Progression Worksheet for Olympiad

Maths Olympiad topic 29: Sequences and AP · Set 955 · 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 5 terms of the AP 7, 10, 13, …? (a) 19 (b) 65 (c) 68 (d) 130
  2. 2.What is the sum of the first 8 odd numbers (1 + 3 + 5 + …)? (a) 15 (b) 72 (c) 64 (d) 36
  3. 3.What is the 30th term of the AP 9, 13, 17, 21, …? (a) 125 (b) 129 (c) 120 (d) 116
  4. 4.What is the 15th term of the AP 7, 9, 11, 13, …? (a) 30 (b) 28 (c) 35 (d) 37
  5. 5.What is the 40th term of the AP 15, 18, 21, 24, …? (a) 132 (b) 135 (c) 120 (d) 117
  6. 6.What is the sum of the first 21 odd numbers (1 + 3 + 5 + …)? (a) 231 (b) 441 (c) 41 (d) 462
  7. 7.What is the missing term in the AP 15, ?, 23, 27, 31? (a) 18 (b) 19 (c) 23 (d) 20
  8. 8.What is the sum of the first 6 odd numbers (1 + 3 + 5 + …)? (a) 21 (b) 42 (c) 36 (d) 11
  9. 9.What is the 16th term of the AP 2, 5, 8, 11, …? (a) 48 (b) 50 (c) 47 (d) 45
  10. 10.What is the missing term in the AP 16, ?, 22, 25, 28? (a) 20 (b) 18 (c) 22 (d) 19
  11. 11.Which term of the AP 7, 12, 17, 22, … is 107? (a) 21st (b) 20th (c) 22nd (d) 23rd
  12. 12.What is the sum of all the whole numbers from 1 to 26? (a) 325 (b) 351 (c) 702 (d) 338
  13. 13.What is the missing term in the AP 1, 7, 13, ?, 25? (a) 19 (b) 18 (c) 20 (d) 25
  14. 14.What is the 15th term of the AP 15, 18, 21, 24, …? (a) 60 (b) 45 (c) 57 (d) 42
  15. 15.What is the missing term in the AP 3, 6, ?, 12, 15? (a) 10 (b) 9 (c) 8 (d) 12
  16. 16.What is the sum of the first 7 terms of the AP 9, 14, 19, …? (a) 336 (b) 173 (c) 39 (d) 168
  17. 17.What is the 10th term of the AP 5, 8, 11, 14, …? (a) 35 (b) 32 (c) 30 (d) 27
  18. 18.What is the 38th term of the AP 6, 8, 10, 12, …? (a) 80 (b) 82 (c) 76 (d) 74
  19. 19.What is the sum of the first 5 odd numbers (1 + 3 + 5 + …)? (a) 15 (b) 9 (c) 30 (d) 25
  20. 20.Which term of the AP 2, 10, 18, 26, … is 250? (a) 32nd (b) 31st (c) 34th (d) 33rd
  21. 21.What is the missing term in the AP 18, 20, 22, ?, 26? (a) 24 (b) 23 (c) 26 (d) 25
  22. 22.What is the sum of the first 20 odd numbers (1 + 3 + 5 + …)? (a) 420 (b) 210 (c) 400 (d) 39
  23. 23.What is the 17th term of the AP 5, 10, 15, 20, …? (a) 85 (b) 80 (c) 86 (d) 90
  24. 24.What is the sum of the first 10 terms of the AP 2, 4, 6, …? (a) 120 (b) 20 (c) 220 (d) 110
  25. 25.What is the sum of the first 5 terms of the AP 4, 10, 16, …? (a) 28 (b) 160 (c) 95 (d) 80
  26. 26.What is the missing term in the AP 16, ?, 34, 43, 52? (a) 24 (b) 26 (c) 34 (d) 25
  27. 27.What is the sum of the first 15 odd numbers (1 + 3 + 5 + …)? (a) 120 (b) 29 (c) 240 (d) 225
  28. 28.What is the missing term in the AP 5, 12, ?, 26, 33? (a) 20 (b) 19 (c) 18 (d) 26
  29. 29.What is the sum of all the whole numbers from 1 to 31? (a) 992 (b) 465 (c) 496 (d) 497
  30. 30.What is the 13th term of the AP 5, 12, 19, 26, …? (a) 91 (b) 96 (c) 89 (d) 84
  31. 31.What is the 29th term of the AP 11, 13, 15, 17, …? (a) 67 (b) 69 (c) 56 (d) 58
  32. 32.What is the sum of the first 6 terms of the AP 2, 5, 8, …? (a) 66 (b) 17 (c) 57 (d) 114
  33. 33.What is the sum of the first 11 terms of the AP 7, 9, 11, …? (a) 374 (b) 27 (c) 198 (d) 187
  34. 34.What is the sum of the first 6 terms of the AP 5, 10, 15, …? (a) 210 (b) 105 (c) 30 (d) 120
  35. 35.What is the missing term in the AP 13, ?, 27, 34, 41? (a) 27 (b) 19 (c) 21 (d) 20
  36. 36.What is the sum of the first 11 terms of the AP 6, 7, 8, …? (a) 242 (b) 122 (c) 16 (d) 121
  37. 37.What is the sum of all the whole numbers from 1 to 59? (a) 1771 (b) 1711 (c) 3540 (d) 1770
  38. 38.Which term of the AP 17, 23, 29, 35, … is 197? (a) 33rd (b) 32nd (c) 31st (d) 30th
  39. 39.Which term of the AP 1, 7, 13, 19, … is 181? (a) 30th (b) 33rd (c) 32nd (d) 31st
  40. 40.What is the missing term in the AP 15, 20, 25, ?, 35? (a) 31 (b) 35 (c) 30 (d) 29

Answer key

  1. 65
  2. 64
  3. 125
  4. 35
  5. 132
  6. 441
  7. 19
  8. 36
  9. 47
  10. 19
  11. 21st
  12. 351
  13. 19
  14. 57
  15. 9
  16. 168
  17. 32
  18. 80
  19. 25
  20. 32nd
  21. 24
  22. 400
  23. 85
  24. 110
  25. 80
  26. 25
  27. 225
  28. 19
  29. 496
  30. 89
  31. 67
  32. 57
  33. 187
  34. 105
  35. 20
  36. 121
  37. 1770
  38. 31st
  39. 31st
  40. 30

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