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Arithmetic Progression Worksheet for Olympiad

Maths Olympiad topic 29: Sequences and AP · Set 352 · 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 26 odd numbers (1 + 3 + 5 + …)? (a) 351 (b) 702 (c) 51 (d) 676
  2. 2.What is the sum of the first 6 odd numbers (1 + 3 + 5 + …)? (a) 21 (b) 42 (c) 36 (d) 11
  3. 3.What is the sum of the first 5 terms of the AP 2, 6, 10, …? (a) 60 (b) 50 (c) 18 (d) 100
  4. 4.What is the 28th term of the AP 1, 5, 9, 13, …? (a) 112 (b) 113 (c) 109 (d) 108
  5. 5.What is the sum of the first 7 terms of the AP 1, 7, 13, …? (a) 37 (b) 133 (c) 154 (d) 266
  6. 6.What is the sum of the first 11 odd numbers (1 + 3 + 5 + …)? (a) 21 (b) 121 (c) 66 (d) 132
  7. 7.What is the sum of the first 8 terms of the AP 8, 12, 16, …? (a) 352 (b) 176 (c) 36 (d) 192
  8. 8.What is the 19th term of the AP 2, 5, 8, 11, …? (a) 57 (b) 59 (c) 56 (d) 54
  9. 9.What is the sum of all the whole numbers from 1 to 96? (a) 4560 (b) 9312 (c) 4608 (d) 4656
  10. 10.What is the sum of the first 5 terms of the AP 10, 15, 20, …? (a) 100 (b) 105 (c) 200 (d) 30
  11. 11.What is the missing term in the AP 4, 13, 22, ?, 40? (a) 30 (b) 32 (c) 40 (d) 31
  12. 12.What is the sum of the first 6 terms of the AP 5, 11, 17, …? (a) 138 (b) 35 (c) 120 (d) 240
  13. 13.What is the 28th term of the AP 15, 20, 25, 30, …? (a) 140 (b) 155 (c) 135 (d) 150
  14. 14.What is the 20th term of the AP 1, 7, 13, 19, …? (a) 121 (b) 115 (c) 120 (d) 114
  15. 15.What is the missing term in the AP 19, ?, 35, 43, 51? (a) 35 (b) 26 (c) 27 (d) 28
  16. 16.What is the sum of the first 9 odd numbers (1 + 3 + 5 + …)? (a) 81 (b) 17 (c) 90 (d) 45
  17. 17.What is the sum of the first 10 terms of the AP 8, 13, 18, …? (a) 610 (b) 53 (c) 330 (d) 305
  18. 18.What is the sum of the first 12 terms of the AP 8, 14, 20, …? (a) 74 (b) 984 (c) 528 (d) 492
  19. 19.What is the missing term in the AP 20, ?, 26, 29, 32? (a) 23 (b) 24 (c) 26 (d) 22
  20. 20.What is the sum of the first 6 terms of the AP 7, 8, 9, …? (a) 114 (b) 60 (c) 12 (d) 57
  21. 21.Which term of the AP 2, 7, 12, 17, … is 97? (a) 19th (b) 22nd (c) 20th (d) 21st
  22. 22.What is the 19th term of the AP 12, 17, 22, 27, …? (a) 107 (b) 95 (c) 102 (d) 90
  23. 23.What is the sum of the first 14 odd numbers (1 + 3 + 5 + …)? (a) 210 (b) 105 (c) 27 (d) 196
  24. 24.What is the 26th term of the AP 15, 18, 21, 24, …? (a) 75 (b) 93 (c) 90 (d) 78
  25. 25.What is the sum of the first 20 odd numbers (1 + 3 + 5 + …)? (a) 39 (b) 420 (c) 400 (d) 210
  26. 26.What is the 13th term of the AP 6, 10, 14, 18, …? (a) 54 (b) 48 (c) 52 (d) 58
  27. 27.What is the 23rd term of the AP 4, 6, 8, 10, …? (a) 44 (b) 46 (c) 50 (d) 48
  28. 28.What is the sum of all the whole numbers from 1 to 52? (a) 1352 (b) 1326 (c) 1378 (d) 2756
  29. 29.What is the sum of all the whole numbers from 1 to 20? (a) 420 (b) 190 (c) 210 (d) 200
  30. 30.What is the 12th term of the AP 19, 28, 37, 46, …? (a) 108 (b) 99 (c) 127 (d) 118
  31. 31.What is the 23rd term of the AP 18, 23, 28, 33, …? (a) 110 (b) 133 (c) 115 (d) 128
  32. 32.What is the 11th term of the AP 18, 23, 28, 33, …? (a) 73 (b) 55 (c) 68 (d) 50
  33. 33.What is the 31st term of the AP 2, 6, 10, 14, …? (a) 126 (b) 124 (c) 120 (d) 122
  34. 34.What is the sum of the first 8 terms of the AP 7, 10, 13, …? (a) 152 (b) 280 (c) 140 (d) 28
  35. 35.Which term of the AP 15, 17, 19, 21, … is 83? (a) 34th (b) 37th (c) 35th (d) 36th
  36. 36.Which term of the AP 17, 21, 25, 29, … is 81? (a) 19th (b) 16th (c) 18th (d) 17th
  37. 37.What is the 16th term of the AP 8, 17, 26, 35, …? (a) 143 (b) 152 (c) 144 (d) 135
  38. 38.What is the 23rd term of the AP 13, 16, 19, 22, …? (a) 69 (b) 82 (c) 79 (d) 66
  39. 39.What is the 40th term of the AP 16, 23, 30, 37, …? (a) 296 (b) 273 (c) 289 (d) 280
  40. 40.What is the sum of the first 6 terms of the AP 1, 7, 13, …? (a) 96 (b) 192 (c) 114 (d) 31

Answer key

  1. 676
  2. 36
  3. 50
  4. 109
  5. 133
  6. 121
  7. 176
  8. 56
  9. 4656
  10. 100
  11. 31
  12. 120
  13. 150
  14. 115
  15. 27
  16. 81
  17. 305
  18. 492
  19. 23
  20. 57
  21. 20th
  22. 102
  23. 196
  24. 90
  25. 400
  26. 54
  27. 48
  28. 1378
  29. 210
  30. 118
  31. 128
  32. 68
  33. 122
  34. 140
  35. 35th
  36. 17th
  37. 143
  38. 79
  39. 289
  40. 96

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