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Arithmetic Progression Worksheet for Olympiad

Maths Olympiad topic 29: Sequences and AP · Set 593 · 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 9 terms of the AP 4, 10, 16, …? (a) 52 (b) 279 (c) 504 (d) 252
  2. 2.Which term of the AP 19, 23, 27, 31, … is 127? (a) 29th (b) 28th (c) 27th (d) 30th
  3. 3.What is the 32nd term of the AP 10, 16, 22, 28, …? (a) 202 (b) 186 (c) 192 (d) 196
  4. 4.What is the 28th term of the AP 1, 6, 11, 16, …? (a) 140 (b) 141 (c) 136 (d) 135
  5. 5.What is the sum of the first 13 odd numbers (1 + 3 + 5 + …)? (a) 25 (b) 182 (c) 91 (d) 169
  6. 6.What is the missing term in the AP 18, ?, 22, 24, 26? (a) 22 (b) 21 (c) 19 (d) 20
  7. 7.What is the sum of the first 6 terms of the AP 7, 10, 13, …? (a) 174 (b) 22 (c) 87 (d) 96
  8. 8.What is the 18th term of the AP 4, 8, 12, 16, …? (a) 72 (b) 73 (c) 68 (d) 76
  9. 9.What is the sum of the first 9 odd numbers (1 + 3 + 5 + …)? (a) 17 (b) 90 (c) 45 (d) 81
  10. 10.What is the sum of all the whole numbers from 1 to 50? (a) 1225 (b) 1250 (c) 2550 (d) 1275
  11. 11.What is the 11th term of the AP 11, 19, 27, 35, …? (a) 91 (b) 80 (c) 99 (d) 88
  12. 12.What is the 35th term of the AP 3, 9, 15, 21, …? (a) 207 (b) 210 (c) 204 (d) 213
  13. 13.What is the sum of the first 11 terms of the AP 2, 6, 10, …? (a) 484 (b) 264 (c) 42 (d) 242
  14. 14.What is the sum of the first 24 odd numbers (1 + 3 + 5 + …)? (a) 300 (b) 47 (c) 600 (d) 576
  15. 15.What is the 13th term of the AP 14, 19, 24, 29, …? (a) 60 (b) 65 (c) 74 (d) 79
  16. 16.What is the sum of the first 7 terms of the AP 7, 12, 17, …? (a) 37 (b) 308 (c) 159 (d) 154
  17. 17.What is the sum of all the whole numbers from 1 to 78? (a) 6162 (b) 3003 (c) 3081 (d) 3042
  18. 18.What is the sum of the first 8 terms of the AP 3, 7, 11, …? (a) 272 (b) 136 (c) 31 (d) 152
  19. 19.What is the 12th term of the AP 6, 12, 18, 24, …? (a) 78 (b) 72 (c) 73 (d) 66
  20. 20.What is the missing term in the AP 20, 29, 38, ?, 56? (a) 48 (b) 46 (c) 56 (d) 47
  21. 21.What is the 25th term of the AP 8, 12, 16, 20, …? (a) 100 (b) 96 (c) 104 (d) 108
  22. 22.What is the sum of the first 18 odd numbers (1 + 3 + 5 + …)? (a) 324 (b) 35 (c) 342 (d) 171
  23. 23.What is the sum of the first 7 terms of the AP 4, 7, 10, …? (a) 91 (b) 22 (c) 182 (d) 94
  24. 24.What is the sum of the first 9 terms of the AP 3, 9, 15, …? (a) 51 (b) 243 (c) 486 (d) 270
  25. 25.What is the sum of all the whole numbers from 1 to 72? (a) 2628 (b) 5256 (c) 2556 (d) 2592
  26. 26.What is the missing term in the AP 1, ?, 19, 28, 37? (a) 19 (b) 9 (c) 11 (d) 10
  27. 27.What is the sum of the first 5 odd numbers (1 + 3 + 5 + …)? (a) 9 (b) 30 (c) 25 (d) 15
  28. 28.Which term of the AP 6, 11, 16, 21, … is 71? (a) 15th (b) 13th (c) 16th (d) 14th
  29. 29.What is the missing term in the AP 16, ?, 22, 25, 28? (a) 22 (b) 19 (c) 20 (d) 18
  30. 30.What is the sum of the first 6 terms of the AP 7, 12, 17, …? (a) 132 (b) 32 (c) 117 (d) 234
  31. 31.What is the missing term in the AP 16, 22, ?, 34, 40? (a) 34 (b) 27 (c) 28 (d) 29
  32. 32.What is the 40th term of the AP 16, 23, 30, 37, …? (a) 296 (b) 273 (c) 289 (d) 280
  33. 33.What is the 27th term of the AP 11, 18, 25, 32, …? (a) 193 (b) 200 (c) 189 (d) 182
  34. 34.What is the 37th term of the AP 6, 8, 10, 12, …? (a) 74 (b) 78 (c) 80 (d) 72
  35. 35.Which term of the AP 13, 19, 25, 31, … is 169? (a) 29th (b) 27th (c) 26th (d) 28th
  36. 36.What is the sum of all the whole numbers from 1 to 91? (a) 4186 (b) 4187 (c) 8372 (d) 4095
  37. 37.What is the missing term in the AP 15, ?, 29, 36, 43? (a) 29 (b) 22 (c) 23 (d) 21
  38. 38.What is the 26th term of the AP 18, 24, 30, 36, …? (a) 156 (b) 150 (c) 174 (d) 168
  39. 39.What is the sum of all the whole numbers from 1 to 16? (a) 272 (b) 120 (c) 136 (d) 128
  40. 40.What is the 36th term of the AP 16, 25, 34, 43, …? (a) 315 (b) 324 (c) 331 (d) 340

Answer key

  1. 252
  2. 28th
  3. 196
  4. 136
  5. 169
  6. 20
  7. 87
  8. 72
  9. 81
  10. 1275
  11. 91
  12. 207
  13. 242
  14. 576
  15. 74
  16. 154
  17. 3081
  18. 136
  19. 72
  20. 47
  21. 104
  22. 324
  23. 91
  24. 243
  25. 2628
  26. 10
  27. 25
  28. 14th
  29. 19
  30. 117
  31. 28
  32. 289
  33. 193
  34. 78
  35. 27th
  36. 4186
  37. 22
  38. 168
  39. 136
  40. 331

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