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Arithmetic Progression Worksheet for Olympiad

Maths Olympiad topic 29: Sequences and AP · Set 145 · 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 5 terms of the AP 10, 16, 22, …? (a) 125 (b) 110 (c) 34 (d) 220
  2. 2.What is the sum of the first 9 terms of the AP 10, 15, 20, …? (a) 50 (b) 540 (c) 270 (d) 275
  3. 3.What is the missing term in the AP 12, 14, ?, 18, 20? (a) 16 (b) 17 (c) 15 (d) 18
  4. 4.What is the 24th term of the AP 4, 7, 10, 13, …? (a) 72 (b) 69 (c) 76 (d) 73
  5. 5.What is the 16th term of the AP 2, 9, 16, 23, …? (a) 107 (b) 112 (c) 114 (d) 105
  6. 6.What is the sum of all the whole numbers from 1 to 21? (a) 231 (b) 232 (c) 462 (d) 210
  7. 7.What is the missing term in the AP 16, 23, ?, 37, 44? (a) 37 (b) 31 (c) 29 (d) 30
  8. 8.What is the sum of the first 9 terms of the AP 1, 5, 9, …? (a) 306 (b) 33 (c) 171 (d) 153
  9. 9.What is the missing term in the AP 10, 14, 18, ?, 26? (a) 21 (b) 26 (c) 23 (d) 22
  10. 10.What is the 13th term of the AP 12, 15, 18, 21, …? (a) 36 (b) 51 (c) 48 (d) 39
  11. 11.What is the sum of all the whole numbers from 1 to 25? (a) 325 (b) 326 (c) 650 (d) 300
  12. 12.What is the missing term in the AP 4, ?, 10, 13, 16? (a) 10 (b) 7 (c) 8 (d) 6
  13. 13.What is the sum of the first 7 terms of the AP 2, 6, 10, …? (a) 112 (b) 98 (c) 26 (d) 196
  14. 14.What is the 21st term of the AP 8, 17, 26, 35, …? (a) 189 (b) 197 (c) 188 (d) 180
  15. 15.What is the sum of all the whole numbers from 1 to 49? (a) 1226 (b) 1225 (c) 2450 (d) 1176
  16. 16.What is the sum of the first 30 odd numbers (1 + 3 + 5 + …)? (a) 59 (b) 465 (c) 930 (d) 900
  17. 17.What is the 32nd term of the AP 7, 10, 13, 16, …? (a) 96 (b) 100 (c) 103 (d) 93
  18. 18.What is the sum of the first 6 terms of the AP 6, 12, 18, …? (a) 126 (b) 252 (c) 144 (d) 36
  19. 19.Which term of the AP 10, 14, 18, 22, … is 138? (a) 35th (b) 32nd (c) 33rd (d) 34th
  20. 20.What is the sum of the first 13 odd numbers (1 + 3 + 5 + …)? (a) 182 (b) 25 (c) 91 (d) 169
  21. 21.What is the sum of the first 6 terms of the AP 7, 10, 13, …? (a) 96 (b) 22 (c) 174 (d) 87
  22. 22.What is the missing term in the AP 6, ?, 12, 15, 18? (a) 8 (b) 12 (c) 9 (d) 10
  23. 23.What is the sum of the first 8 terms of the AP 10, 15, 20, …? (a) 240 (b) 45 (c) 440 (d) 220
  24. 24.What is the 19th term of the AP 9, 16, 23, 30, …? (a) 142 (b) 126 (c) 133 (d) 135
  25. 25.What is the 27th term of the AP 4, 7, 10, 13, …? (a) 82 (b) 85 (c) 81 (d) 78
  26. 26.What is the sum of the first 7 terms of the AP 6, 7, 8, …? (a) 12 (b) 64 (c) 63 (d) 126
  27. 27.Which term of the AP 3, 10, 17, 24, … is 80? (a) 13th (b) 11th (c) 14th (d) 12th
  28. 28.What is the sum of the first 8 terms of the AP 1, 7, 13, …? (a) 43 (b) 352 (c) 200 (d) 176
  29. 29.What is the sum of the first 12 terms of the AP 7, 11, 15, …? (a) 696 (b) 372 (c) 51 (d) 348
  30. 30.What is the 24th term of the AP 14, 17, 20, 23, …? (a) 86 (b) 83 (c) 69 (d) 72
  31. 31.What is the 12th term of the AP 18, 21, 24, 27, …? (a) 33 (b) 36 (c) 54 (d) 51
  32. 32.What is the 12th term of the AP 4, 7, 10, 13, …? (a) 40 (b) 33 (c) 37 (d) 36
  33. 33.What is the sum of all the whole numbers from 1 to 16? (a) 120 (b) 136 (c) 128 (d) 272
  34. 34.What is the sum of the first 7 terms of the AP 4, 10, 16, …? (a) 154 (b) 175 (c) 40 (d) 308
  35. 35.What is the sum of the first 12 terms of the AP 4, 8, 12, …? (a) 312 (b) 624 (c) 336 (d) 48
  36. 36.What is the 32nd term of the AP 17, 26, 35, 44, …? (a) 296 (b) 288 (c) 305 (d) 279
  37. 37.What is the missing term in the AP 3, ?, 21, 30, 39? (a) 12 (b) 21 (c) 11 (d) 13
  38. 38.What is the sum of the first 12 terms of the AP 4, 6, 8, …? (a) 26 (b) 360 (c) 192 (d) 180
  39. 39.What is the sum of all the whole numbers from 1 to 91? (a) 4186 (b) 4095 (c) 8372 (d) 4187
  40. 40.What is the sum of all the whole numbers from 1 to 73? (a) 2628 (b) 2702 (c) 5402 (d) 2701

Answer key

  1. 110
  2. 270
  3. 16
  4. 73
  5. 107
  6. 231
  7. 30
  8. 153
  9. 22
  10. 48
  11. 325
  12. 7
  13. 98
  14. 188
  15. 1225
  16. 900
  17. 100
  18. 126
  19. 33rd
  20. 169
  21. 87
  22. 9
  23. 220
  24. 135
  25. 82
  26. 63
  27. 12th
  28. 176
  29. 348
  30. 83
  31. 51
  32. 37
  33. 136
  34. 154
  35. 312
  36. 296
  37. 12
  38. 180
  39. 4186
  40. 2701

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