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Arithmetic Progression Worksheet for Olympiad

Maths Olympiad topic 29: Sequences and AP · Set 223 · 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 27th term of the AP 20, 29, 38, 47, …? (a) 254 (b) 263 (c) 243 (d) 234
  2. 2.Which term of the AP 2, 11, 20, 29, … is 263? (a) 32nd (b) 30th (c) 31st (d) 29th
  3. 3.What is the sum of the first 11 terms of the AP 10, 12, 14, …? (a) 440 (b) 30 (c) 220 (d) 231
  4. 4.What is the 27th term of the AP 3, 10, 17, 24, …? (a) 192 (b) 189 (c) 182 (d) 185
  5. 5.What is the 33rd term of the AP 7, 11, 15, 19, …? (a) 132 (b) 139 (c) 135 (d) 128
  6. 6.What is the 38th term of the AP 6, 9, 12, 15, …? (a) 111 (b) 114 (c) 117 (d) 120
  7. 7.What is the sum of all the whole numbers from 1 to 35? (a) 595 (b) 1260 (c) 631 (d) 630
  8. 8.Which term of the AP 6, 8, 10, 12, … is 32? (a) 16th (b) 13th (c) 14th (d) 15th
  9. 9.What is the sum of the first 5 terms of the AP 1, 4, 7, …? (a) 35 (b) 13 (c) 38 (d) 70
  10. 10.What is the sum of the first 17 odd numbers (1 + 3 + 5 + …)? (a) 306 (b) 33 (c) 153 (d) 289
  11. 11.What is the sum of all the whole numbers from 1 to 56? (a) 1596 (b) 3192 (c) 1540 (d) 1568
  12. 12.What is the sum of all the whole numbers from 1 to 10? (a) 45 (b) 55 (c) 110 (d) 50
  13. 13.What is the 35th term of the AP 10, 13, 16, 19, …? (a) 102 (b) 115 (c) 112 (d) 105
  14. 14.What is the 21st term of the AP 1, 4, 7, 10, …? (a) 63 (b) 60 (c) 64 (d) 61
  15. 15.What is the sum of the first 25 odd numbers (1 + 3 + 5 + …)? (a) 650 (b) 625 (c) 49 (d) 325
  16. 16.What is the sum of the first 8 terms of the AP 1, 4, 7, …? (a) 184 (b) 22 (c) 92 (d) 104
  17. 17.What is the sum of all the whole numbers from 1 to 78? (a) 6162 (b) 3003 (c) 3042 (d) 3081
  18. 18.What is the missing term in the AP 6, ?, 18, 24, 30? (a) 12 (b) 13 (c) 11 (d) 18
  19. 19.What is the 10th term of the AP 20, 23, 26, 29, …? (a) 50 (b) 47 (c) 27 (d) 30
  20. 20.What is the sum of the first 18 odd numbers (1 + 3 + 5 + …)? (a) 342 (b) 35 (c) 171 (d) 324
  21. 21.What is the sum of the first 9 terms of the AP 6, 8, 10, …? (a) 252 (b) 126 (c) 135 (d) 22
  22. 22.What is the missing term in the AP 3, 7, ?, 15, 19? (a) 11 (b) 12 (c) 10 (d) 15
  23. 23.What is the sum of all the whole numbers from 1 to 76? (a) 2850 (b) 2888 (c) 5852 (d) 2926
  24. 24.What is the sum of the first 12 odd numbers (1 + 3 + 5 + …)? (a) 156 (b) 78 (c) 144 (d) 23
  25. 25.What is the sum of the first 9 terms of the AP 2, 7, 12, …? (a) 396 (b) 203 (c) 42 (d) 198
  26. 26.What is the missing term in the AP 10, 19, ?, 37, 46? (a) 37 (b) 27 (c) 29 (d) 28
  27. 27.What is the missing term in the AP 7, 15, ?, 31, 39? (a) 22 (b) 23 (c) 24 (d) 31
  28. 28.What is the sum of the first 10 terms of the AP 1, 7, 13, …? (a) 55 (b) 280 (c) 310 (d) 560
  29. 29.What is the 30th term of the AP 1, 10, 19, 28, …? (a) 261 (b) 271 (c) 262 (d) 270
  30. 30.What is the sum of all the whole numbers from 1 to 49? (a) 1176 (b) 1226 (c) 1225 (d) 2450
  31. 31.What is the sum of the first 10 terms of the AP 7, 9, 11, …? (a) 25 (b) 170 (c) 320 (d) 160
  32. 32.What is the 11th term of the AP 6, 10, 14, 18, …? (a) 50 (b) 40 (c) 46 (d) 44
  33. 33.What is the 17th term of the AP 12, 20, 28, 36, …? (a) 128 (b) 136 (c) 148 (d) 140
  34. 34.What is the 26th term of the AP 17, 26, 35, 44, …? (a) 242 (b) 225 (c) 234 (d) 251
  35. 35.What is the sum of the first 9 terms of the AP 6, 9, 12, …? (a) 30 (b) 162 (c) 165 (d) 324
  36. 36.Which term of the AP 14, 18, 22, 26, … is 42? (a) 8th (b) 10th (c) 7th (d) 9th
  37. 37.What is the 22nd term of the AP 19, 23, 27, 31, …? (a) 107 (b) 103 (c) 84 (d) 88
  38. 38.What is the 27th term of the AP 8, 15, 22, 29, …? (a) 190 (b) 182 (c) 197 (d) 189
  39. 39.Which term of the AP 8, 11, 14, 17, … is 62? (a) 19th (b) 21st (c) 20th (d) 18th
  40. 40.What is the 13th term of the AP 4, 11, 18, 25, …? (a) 91 (b) 95 (c) 84 (d) 88

Answer key

  1. 254
  2. 30th
  3. 220
  4. 185
  5. 135
  6. 117
  7. 630
  8. 14th
  9. 35
  10. 289
  11. 1596
  12. 55
  13. 112
  14. 61
  15. 625
  16. 92
  17. 3081
  18. 12
  19. 47
  20. 324
  21. 126
  22. 11
  23. 2926
  24. 144
  25. 198
  26. 28
  27. 23
  28. 280
  29. 262
  30. 1225
  31. 160
  32. 46
  33. 140
  34. 242
  35. 162
  36. 8th
  37. 103
  38. 190
  39. 19th
  40. 88

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