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Arithmetic Progression Worksheet for Olympiad

Maths Olympiad topic 29: Sequences and AP · Set 681 · 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 all the whole numbers from 1 to 52? (a) 2756 (b) 1378 (c) 1352 (d) 1326
  2. 2.What is the missing term in the AP 2, 11, ?, 29, 38? (a) 21 (b) 19 (c) 20 (d) 29
  3. 3.What is the sum of the first 5 terms of the AP 9, 15, 21, …? (a) 210 (b) 120 (c) 105 (d) 33
  4. 4.What is the missing term in the AP 19, ?, 37, 46, 55? (a) 37 (b) 28 (c) 27 (d) 29
  5. 5.What is the sum of the first 5 terms of the AP 8, 11, 14, …? (a) 140 (b) 20 (c) 70 (d) 73
  6. 6.What is the sum of the first 9 terms of the AP 7, 10, 13, …? (a) 174 (b) 342 (c) 31 (d) 171
  7. 7.What is the missing term in the AP 8, 10, 12, ?, 16? (a) 16 (b) 15 (c) 14 (d) 13
  8. 8.What is the sum of the first 9 terms of the AP 2, 3, 4, …? (a) 55 (b) 108 (c) 10 (d) 54
  9. 9.What is the missing term in the AP 13, 22, ?, 40, 49? (a) 30 (b) 31 (c) 40 (d) 32
  10. 10.What is the sum of the first 10 terms of the AP 9, 15, 21, …? (a) 390 (b) 63 (c) 360 (d) 720
  11. 11.What is the sum of the first 11 terms of the AP 8, 14, 20, …? (a) 451 (b) 836 (c) 418 (d) 68
  12. 12.What is the sum of the first 10 terms of the AP 1, 4, 7, …? (a) 28 (b) 160 (c) 145 (d) 290
  13. 13.What is the 11th term of the AP 7, 10, 13, 16, …? (a) 40 (b) 37 (c) 33 (d) 30
  14. 14.Which term of the AP 4, 9, 14, 19, … is 104? (a) 23rd (b) 21st (c) 20th (d) 22nd
  15. 15.What is the sum of the first 9 terms of the AP 6, 11, 16, …? (a) 239 (b) 46 (c) 234 (d) 468
  16. 16.What is the sum of the first 21 odd numbers (1 + 3 + 5 + …)? (a) 231 (b) 462 (c) 441 (d) 41
  17. 17.What is the sum of the first 6 terms of the AP 1, 2, 3, …? (a) 6 (b) 42 (c) 21 (d) 24
  18. 18.What is the sum of all the whole numbers from 1 to 62? (a) 1922 (b) 1891 (c) 1953 (d) 3906
  19. 19.What is the 30th term of the AP 5, 7, 9, 11, …? (a) 65 (b) 60 (c) 63 (d) 58
  20. 20.What is the 14th term of the AP 13, 21, 29, 37, …? (a) 125 (b) 112 (c) 117 (d) 104
  21. 21.What is the 20th term of the AP 2, 6, 10, 14, …? (a) 78 (b) 82 (c) 76 (d) 80
  22. 22.What is the sum of all the whole numbers from 1 to 61? (a) 3782 (b) 1830 (c) 1892 (d) 1891
  23. 23.What is the sum of all the whole numbers from 1 to 51? (a) 1327 (b) 2652 (c) 1326 (d) 1275
  24. 24.What is the missing term in the AP 8, 17, 26, ?, 44? (a) 44 (b) 35 (c) 36 (d) 34
  25. 25.What is the sum of the first 12 terms of the AP 9, 11, 13, …? (a) 252 (b) 31 (c) 480 (d) 240
  26. 26.What is the sum of the first 11 terms of the AP 4, 5, 6, …? (a) 100 (b) 99 (c) 14 (d) 198
  27. 27.What is the sum of the first 5 terms of the AP 1, 7, 13, …? (a) 80 (b) 65 (c) 25 (d) 130
  28. 28.What is the sum of the first 14 odd numbers (1 + 3 + 5 + …)? (a) 105 (b) 210 (c) 196 (d) 27
  29. 29.What is the 28th term of the AP 17, 21, 25, 29, …? (a) 129 (b) 108 (c) 125 (d) 112
  30. 30.What is the sum of the first 6 terms of the AP 4, 6, 8, …? (a) 14 (b) 108 (c) 54 (d) 60
  31. 31.Which term of the AP 17, 21, 25, 29, … is 125? (a) 28th (b) 27th (c) 29th (d) 30th
  32. 32.What is the 13th term of the AP 5, 13, 21, 29, …? (a) 104 (b) 109 (c) 96 (d) 101
  33. 33.Which term of the AP 10, 14, 18, 22, … is 154? (a) 37th (b) 38th (c) 36th (d) 39th
  34. 34.What is the missing term in the AP 12, ?, 30, 39, 48? (a) 30 (b) 22 (c) 21 (d) 20
  35. 35.What is the sum of the first 16 odd numbers (1 + 3 + 5 + …)? (a) 136 (b) 256 (c) 31 (d) 272
  36. 36.What is the 33rd term of the AP 3, 7, 11, 15, …? (a) 128 (b) 132 (c) 131 (d) 135
  37. 37.What is the sum of the first 7 terms of the AP 9, 15, 21, …? (a) 189 (b) 210 (c) 378 (d) 45
  38. 38.Which term of the AP 7, 11, 15, 19, … is 115? (a) 27th (b) 30th (c) 29th (d) 28th
  39. 39.What is the 22nd term of the AP 12, 18, 24, 30, …? (a) 138 (b) 144 (c) 126 (d) 132
  40. 40.What is the sum of the first 10 terms of the AP 6, 8, 10, …? (a) 160 (b) 300 (c) 24 (d) 150

Answer key

  1. 1378
  2. 20
  3. 105
  4. 28
  5. 70
  6. 171
  7. 14
  8. 54
  9. 31
  10. 360
  11. 418
  12. 145
  13. 37
  14. 21st
  15. 234
  16. 441
  17. 21
  18. 1953
  19. 63
  20. 117
  21. 78
  22. 1891
  23. 1326
  24. 35
  25. 240
  26. 99
  27. 65
  28. 196
  29. 125
  30. 54
  31. 28th
  32. 101
  33. 37th
  34. 21
  35. 256
  36. 131
  37. 189
  38. 28th
  39. 138
  40. 150

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