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Arithmetic Progression Worksheet for Olympiad

Maths Olympiad topic 29: Sequences and AP · Set 908 · 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 44? (a) 1980 (b) 946 (c) 968 (d) 990
  2. 2.What is the 33rd term of the AP 9, 13, 17, 21, …? (a) 132 (b) 141 (c) 137 (d) 128
  3. 3.What is the 33rd term of the AP 16, 20, 24, 28, …? (a) 144 (b) 128 (c) 148 (d) 132
  4. 4.What is the 20th term of the AP 3, 11, 19, 27, …? (a) 160 (b) 152 (c) 155 (d) 163
  5. 5.What is the missing term in the AP 20, ?, 38, 47, 56? (a) 30 (b) 28 (c) 29 (d) 38
  6. 6.What is the sum of all the whole numbers from 1 to 91? (a) 4187 (b) 8372 (c) 4095 (d) 4186
  7. 7.What is the 10th term of the AP 1, 4, 7, 10, …? (a) 30 (b) 31 (c) 28 (d) 27
  8. 8.What is the missing term in the AP 5, ?, 21, 29, 37? (a) 21 (b) 12 (c) 13 (d) 14
  9. 9.What is the 15th term of the AP 5, 7, 9, 11, …? (a) 33 (b) 28 (c) 35 (d) 30
  10. 10.What is the 21st term of the AP 13, 17, 21, 25, …? (a) 84 (b) 93 (c) 80 (d) 97
  11. 11.What is the sum of the first 13 odd numbers (1 + 3 + 5 + …)? (a) 169 (b) 91 (c) 182 (d) 25
  12. 12.What is the sum of the first 12 terms of the AP 1, 3, 5, …? (a) 23 (b) 156 (c) 144 (d) 288
  13. 13.What is the sum of the first 5 terms of the AP 3, 7, 11, …? (a) 19 (b) 110 (c) 65 (d) 55
  14. 14.What is the sum of the first 28 odd numbers (1 + 3 + 5 + …)? (a) 55 (b) 812 (c) 406 (d) 784
  15. 15.What is the missing term in the AP 7, ?, 21, 28, 35? (a) 14 (b) 21 (c) 13 (d) 15
  16. 16.What is the 20th term of the AP 19, 26, 33, 40, …? (a) 159 (b) 133 (c) 140 (d) 152
  17. 17.What is the sum of the first 9 terms of the AP 6, 9, 12, …? (a) 30 (b) 324 (c) 165 (d) 162
  18. 18.What is the sum of the first 5 terms of the AP 2, 6, 10, …? (a) 18 (b) 50 (c) 60 (d) 100
  19. 19.What is the 29th term of the AP 15, 20, 25, 30, …? (a) 160 (b) 140 (c) 155 (d) 145
  20. 20.What is the sum of the first 7 terms of the AP 10, 11, 12, …? (a) 91 (b) 16 (c) 182 (d) 92
  21. 21.What is the sum of the first 7 terms of the AP 3, 6, 9, …? (a) 84 (b) 21 (c) 168 (d) 87
  22. 22.What is the 16th term of the AP 3, 5, 7, 9, …? (a) 32 (b) 30 (c) 33 (d) 35
  23. 23.What is the sum of the first 9 terms of the AP 7, 10, 13, …? (a) 342 (b) 174 (c) 31 (d) 171
  24. 24.What is the sum of the first 10 terms of the AP 6, 9, 12, …? (a) 390 (b) 33 (c) 210 (d) 195
  25. 25.What is the sum of the first 9 terms of the AP 7, 9, 11, …? (a) 270 (b) 23 (c) 135 (d) 144
  26. 26.What is the missing term in the AP 18, 27, ?, 45, 54? (a) 45 (b) 36 (c) 37 (d) 35
  27. 27.What is the 11th term of the AP 6, 11, 16, 21, …? (a) 50 (b) 55 (c) 61 (d) 56
  28. 28.What is the 27th term of the AP 2, 5, 8, 11, …? (a) 80 (b) 83 (c) 78 (d) 81
  29. 29.Which term of the AP 8, 16, 24, 32, … is 240? (a) 31st (b) 30th (c) 29th (d) 32nd
  30. 30.What is the missing term in the AP 13, 21, ?, 37, 45? (a) 30 (b) 37 (c) 29 (d) 28
  31. 31.What is the sum of all the whole numbers from 1 to 92? (a) 8556 (b) 4232 (c) 4278 (d) 4186
  32. 32.What is the sum of the first 15 odd numbers (1 + 3 + 5 + …)? (a) 240 (b) 225 (c) 120 (d) 29
  33. 33.What is the sum of the first 8 terms of the AP 8, 13, 18, …? (a) 43 (b) 204 (c) 224 (d) 408
  34. 34.What is the missing term in the AP 14, 16, 18, ?, 22? (a) 21 (b) 22 (c) 19 (d) 20
  35. 35.What is the 22nd term of the AP 20, 25, 30, 35, …? (a) 105 (b) 125 (c) 110 (d) 130
  36. 36.What is the missing term in the AP 9, 12, ?, 18, 21? (a) 15 (b) 16 (c) 14 (d) 18
  37. 37.What is the missing term in the AP 10, ?, 22, 28, 34? (a) 15 (b) 17 (c) 22 (d) 16
  38. 38.What is the 18th term of the AP 3, 11, 19, 27, …? (a) 147 (b) 139 (c) 144 (d) 136
  39. 39.What is the sum of the first 6 terms of the AP 5, 7, 9, …? (a) 66 (b) 60 (c) 15 (d) 120
  40. 40.What is the sum of all the whole numbers from 1 to 84? (a) 3486 (b) 7140 (c) 3528 (d) 3570

Answer key

  1. 990
  2. 137
  3. 144
  4. 155
  5. 29
  6. 4186
  7. 28
  8. 13
  9. 33
  10. 93
  11. 169
  12. 144
  13. 55
  14. 784
  15. 14
  16. 152
  17. 162
  18. 50
  19. 155
  20. 91
  21. 84
  22. 33
  23. 171
  24. 195
  25. 135
  26. 36
  27. 56
  28. 80
  29. 30th
  30. 29
  31. 4278
  32. 225
  33. 204
  34. 20
  35. 125
  36. 15
  37. 16
  38. 139
  39. 60
  40. 3570

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