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Arithmetic Progression Worksheet for Olympiad

Maths Olympiad topic 29: Sequences and AP · Set 217 · 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 20th term of the AP 8, 13, 18, 23, …? (a) 108 (b) 103 (c) 100 (d) 95
  2. 2.What is the sum of the first 5 terms of the AP 7, 11, 15, …? (a) 23 (b) 150 (c) 85 (d) 75
  3. 3.What is the sum of the first 8 terms of the AP 5, 9, 13, …? (a) 168 (b) 152 (c) 33 (d) 304
  4. 4.What is the missing term in the AP 20, 22, ?, 26, 28? (a) 26 (b) 25 (c) 24 (d) 23
  5. 5.What is the 32nd term of the AP 18, 21, 24, 27, …? (a) 96 (b) 114 (c) 111 (d) 93
  6. 6.Which term of the AP 17, 20, 23, 26, … is 107? (a) 30th (b) 32nd (c) 33rd (d) 31st
  7. 7.What is the 24th term of the AP 7, 14, 21, 28, …? (a) 175 (b) 169 (c) 161 (d) 168
  8. 8.Which term of the AP 11, 15, 19, 23, … is 155? (a) 36th (b) 39th (c) 38th (d) 37th
  9. 9.Which term of the AP 5, 12, 19, 26, … is 264? (a) 39th (b) 40th (c) 37th (d) 38th
  10. 10.What is the sum of all the whole numbers from 1 to 13? (a) 91 (b) 182 (c) 92 (d) 78
  11. 11.What is the sum of the first 7 terms of the AP 2, 4, 6, …? (a) 56 (b) 63 (c) 14 (d) 112
  12. 12.What is the sum of the first 10 terms of the AP 2, 6, 10, …? (a) 200 (b) 220 (c) 38 (d) 400
  13. 13.What is the 13th term of the AP 11, 20, 29, 38, …? (a) 119 (b) 117 (c) 128 (d) 108
  14. 14.What is the sum of the first 6 terms of the AP 5, 11, 17, …? (a) 35 (b) 240 (c) 138 (d) 120
  15. 15.What is the sum of the first 5 odd numbers (1 + 3 + 5 + …)? (a) 30 (b) 25 (c) 9 (d) 15
  16. 16.What is the 10th term of the AP 8, 15, 22, 29, …? (a) 71 (b) 63 (c) 78 (d) 70
  17. 17.What is the 23rd term of the AP 19, 27, 35, 43, …? (a) 203 (b) 184 (c) 195 (d) 176
  18. 18.Which term of the AP 11, 15, 19, 23, … is 111? (a) 28th (b) 25th (c) 26th (d) 27th
  19. 19.What is the missing term in the AP 13, 20, 27, ?, 41? (a) 34 (b) 33 (c) 35 (d) 41
  20. 20.What is the 12th term of the AP 5, 11, 17, 23, …? (a) 72 (b) 77 (c) 66 (d) 71
  21. 21.What is the sum of the first 6 odd numbers (1 + 3 + 5 + …)? (a) 11 (b) 21 (c) 42 (d) 36
  22. 22.What is the 15th term of the AP 4, 12, 20, 28, …? (a) 112 (b) 120 (c) 116 (d) 124
  23. 23.Which term of the AP 17, 21, 25, 29, … is 105? (a) 23rd (b) 25th (c) 24th (d) 22nd
  24. 24.What is the sum of the first 13 odd numbers (1 + 3 + 5 + …)? (a) 169 (b) 182 (c) 25 (d) 91
  25. 25.What is the sum of all the whole numbers from 1 to 91? (a) 4095 (b) 4187 (c) 8372 (d) 4186
  26. 26.What is the 16th term of the AP 11, 13, 15, 17, …? (a) 43 (b) 41 (c) 32 (d) 30
  27. 27.What is the sum of all the whole numbers from 1 to 69? (a) 4830 (b) 2416 (c) 2415 (d) 2346
  28. 28.What is the sum of the first 26 odd numbers (1 + 3 + 5 + …)? (a) 702 (b) 51 (c) 351 (d) 676
  29. 29.What is the missing term in the AP 1, ?, 7, 10, 13? (a) 5 (b) 3 (c) 7 (d) 4
  30. 30.What is the 27th term of the AP 3, 11, 19, 27, …? (a) 208 (b) 219 (c) 216 (d) 211
  31. 31.What is the 29th term of the AP 6, 9, 12, 15, …? (a) 84 (b) 87 (c) 93 (d) 90
  32. 32.What is the 18th term of the AP 10, 16, 22, 28, …? (a) 102 (b) 112 (c) 118 (d) 108
  33. 33.What is the missing term in the AP 7, 9, 11, ?, 15? (a) 13 (b) 15 (c) 14 (d) 12
  34. 34.What is the 37th term of the AP 12, 19, 26, 33, …? (a) 271 (b) 264 (c) 259 (d) 252
  35. 35.Which term of the AP 17, 26, 35, 44, … is 350? (a) 39th (b) 40th (c) 37th (d) 38th
  36. 36.What is the missing term in the AP 12, 16, ?, 24, 28? (a) 20 (b) 19 (c) 24 (d) 21
  37. 37.What is the 27th term of the AP 1, 8, 15, 22, …? (a) 182 (b) 183 (c) 190 (d) 189
  38. 38.What is the sum of the first 8 terms of the AP 2, 7, 12, …? (a) 156 (b) 176 (c) 312 (d) 37
  39. 39.What is the missing term in the AP 4, 7, ?, 13, 16? (a) 13 (b) 9 (c) 10 (d) 11
  40. 40.What is the sum of the first 12 terms of the AP 7, 13, 19, …? (a) 480 (b) 960 (c) 73 (d) 516

Answer key

  1. 103
  2. 75
  3. 152
  4. 24
  5. 111
  6. 31st
  7. 168
  8. 37th
  9. 38th
  10. 91
  11. 56
  12. 200
  13. 119
  14. 120
  15. 25
  16. 71
  17. 195
  18. 26th
  19. 34
  20. 71
  21. 36
  22. 116
  23. 23rd
  24. 169
  25. 4186
  26. 41
  27. 2415
  28. 676
  29. 4
  30. 211
  31. 90
  32. 112
  33. 13
  34. 264
  35. 38th
  36. 20
  37. 183
  38. 156
  39. 10
  40. 480

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