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Arithmetic Progression Worksheet for Olympiad

Maths Olympiad topic 29: Sequences and AP · Set 136 · 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 6, 8, 10, …? (a) 18 (b) 84 (c) 168 (d) 91
  2. 2.What is the sum of the first 18 odd numbers (1 + 3 + 5 + …)? (a) 35 (b) 171 (c) 342 (d) 324
  3. 3.What is the sum of the first 6 terms of the AP 2, 5, 8, …? (a) 114 (b) 17 (c) 66 (d) 57
  4. 4.What is the sum of the first 5 odd numbers (1 + 3 + 5 + …)? (a) 25 (b) 9 (c) 30 (d) 15
  5. 5.What is the 22nd term of the AP 13, 17, 21, 25, …? (a) 88 (b) 84 (c) 101 (d) 97
  6. 6.What is the 39th term of the AP 2, 4, 6, 8, …? (a) 76 (b) 79 (c) 78 (d) 80
  7. 7.What is the 15th term of the AP 14, 17, 20, 23, …? (a) 56 (b) 59 (c) 45 (d) 42
  8. 8.What is the sum of the first 11 terms of the AP 10, 12, 14, …? (a) 440 (b) 220 (c) 231 (d) 30
  9. 9.What is the missing term in the AP 10, 17, ?, 31, 38? (a) 25 (b) 31 (c) 24 (d) 23
  10. 10.What is the sum of the first 12 terms of the AP 6, 9, 12, …? (a) 288 (b) 270 (c) 39 (d) 540
  11. 11.What is the 30th term of the AP 11, 15, 19, 23, …? (a) 116 (b) 127 (c) 120 (d) 131
  12. 12.What is the 35th term of the AP 12, 19, 26, 33, …? (a) 257 (b) 250 (c) 245 (d) 238
  13. 13.What is the sum of the first 11 terms of the AP 8, 12, 16, …? (a) 330 (b) 308 (c) 616 (d) 48
  14. 14.What is the 32nd term of the AP 9, 11, 13, 15, …? (a) 71 (b) 73 (c) 64 (d) 62
  15. 15.What is the missing term in the AP 9, ?, 15, 18, 21? (a) 11 (b) 15 (c) 12 (d) 13
  16. 16.What is the sum of the first 10 terms of the AP 3, 5, 7, …? (a) 120 (b) 21 (c) 130 (d) 240
  17. 17.Which term of the AP 1, 4, 7, 10, … is 103? (a) 34th (b) 35th (c) 36th (d) 37th
  18. 18.Which term of the AP 20, 24, 28, 32, … is 136? (a) 31st (b) 29th (c) 30th (d) 34th
  19. 19.What is the sum of the first 6 odd numbers (1 + 3 + 5 + …)? (a) 42 (b) 21 (c) 36 (d) 11
  20. 20.What is the 35th term of the AP 16, 21, 26, 31, …? (a) 191 (b) 170 (c) 186 (d) 175
  21. 21.What is the sum of the first 11 terms of the AP 6, 11, 16, …? (a) 56 (b) 341 (c) 346 (d) 682
  22. 22.What is the 21st term of the AP 9, 15, 21, 27, …? (a) 129 (b) 126 (c) 135 (d) 120
  23. 23.What is the missing term in the AP 6, 13, 20, ?, 34? (a) 34 (b) 26 (c) 27 (d) 28
  24. 24.Which term of the AP 4, 9, 14, 19, … is 159? (a) 33rd (b) 34th (c) 32nd (d) 31st
  25. 25.What is the sum of the first 21 odd numbers (1 + 3 + 5 + …)? (a) 462 (b) 231 (c) 41 (d) 441
  26. 26.What is the sum of the first 5 terms of the AP 9, 10, 11, …? (a) 55 (b) 13 (c) 56 (d) 110
  27. 27.What is the sum of all the whole numbers from 1 to 61? (a) 3782 (b) 1892 (c) 1891 (d) 1830
  28. 28.What is the 12th term of the AP 20, 29, 38, 47, …? (a) 128 (b) 119 (c) 99 (d) 108
  29. 29.What is the sum of the first 12 terms of the AP 9, 14, 19, …? (a) 64 (b) 876 (c) 438 (d) 468
  30. 30.Which term of the AP 8, 12, 16, 20, … is 140? (a) 33rd (b) 35th (c) 36th (d) 34th
  31. 31.What is the sum of the first 9 odd numbers (1 + 3 + 5 + …)? (a) 45 (b) 90 (c) 17 (d) 81
  32. 32.What is the sum of the first 6 terms of the AP 5, 9, 13, …? (a) 25 (b) 180 (c) 102 (d) 90
  33. 33.What is the missing term in the AP 18, 20, 22, ?, 26? (a) 25 (b) 24 (c) 26 (d) 23
  34. 34.What is the missing term in the AP 2, 7, 12, ?, 22? (a) 18 (b) 22 (c) 16 (d) 17
  35. 35.What is the 28th term of the AP 7, 11, 15, 19, …? (a) 108 (b) 112 (c) 119 (d) 115
  36. 36.What is the sum of the first 9 terms of the AP 2, 5, 8, …? (a) 129 (b) 252 (c) 126 (d) 26
  37. 37.Which term of the AP 1, 7, 13, 19, … is 157? (a) 29th (b) 28th (c) 26th (d) 27th
  38. 38.What is the sum of the first 5 terms of the AP 6, 11, 16, …? (a) 80 (b) 160 (c) 85 (d) 26
  39. 39.Which term of the AP 20, 25, 30, 35, … is 215? (a) 41st (b) 39th (c) 40th (d) 43rd
  40. 40.Which term of the AP 8, 11, 14, 17, … is 71? (a) 24th (b) 22nd (c) 23rd (d) 21st

Answer key

  1. 84
  2. 324
  3. 57
  4. 25
  5. 97
  6. 78
  7. 56
  8. 220
  9. 24
  10. 270
  11. 127
  12. 250
  13. 308
  14. 71
  15. 12
  16. 120
  17. 35th
  18. 30th
  19. 36
  20. 186
  21. 341
  22. 129
  23. 27
  24. 32nd
  25. 441
  26. 55
  27. 1891
  28. 119
  29. 438
  30. 34th
  31. 81
  32. 90
  33. 24
  34. 17
  35. 115
  36. 126
  37. 27th
  38. 80
  39. 40th
  40. 22nd

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