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Arithmetic Progression Worksheet for Olympiad

Maths Olympiad topic 29: Sequences and AP · Set 114 · 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 67? (a) 2279 (b) 2278 (c) 2211 (d) 4556
  2. 2.What is the 39th term of the AP 14, 20, 26, 32, …? (a) 228 (b) 248 (c) 242 (d) 234
  3. 3.What is the sum of the first 5 terms of the AP 7, 13, 19, …? (a) 31 (b) 110 (c) 95 (d) 190
  4. 4.What is the sum of the first 21 odd numbers (1 + 3 + 5 + …)? (a) 41 (b) 231 (c) 441 (d) 462
  5. 5.What is the 27th term of the AP 13, 18, 23, 28, …? (a) 130 (b) 148 (c) 135 (d) 143
  6. 6.What is the 38th term of the AP 4, 6, 8, 10, …? (a) 78 (b) 76 (c) 74 (d) 80
  7. 7.What is the sum of the first 8 terms of the AP 9, 12, 15, …? (a) 30 (b) 312 (c) 168 (d) 156
  8. 8.What is the missing term in the AP 9, 15, 21, ?, 33? (a) 27 (b) 28 (c) 26 (d) 33
  9. 9.What is the missing term in the AP 16, ?, 20, 22, 24? (a) 19 (b) 20 (c) 17 (d) 18
  10. 10.What is the sum of the first 9 terms of the AP 2, 5, 8, …? (a) 252 (b) 26 (c) 129 (d) 126
  11. 11.What is the sum of the first 9 terms of the AP 3, 5, 7, …? (a) 99 (b) 198 (c) 19 (d) 108
  12. 12.What is the missing term in the AP 8, 10, ?, 14, 16? (a) 11 (b) 14 (c) 13 (d) 12
  13. 13.What is the sum of the first 7 odd numbers (1 + 3 + 5 + …)? (a) 28 (b) 13 (c) 49 (d) 56
  14. 14.What is the 36th term of the AP 6, 13, 20, 27, …? (a) 258 (b) 245 (c) 251 (d) 252
  15. 15.What is the 11th term of the AP 7, 11, 15, 19, …? (a) 40 (b) 51 (c) 44 (d) 47
  16. 16.Which term of the AP 5, 14, 23, 32, … is 95? (a) 11th (b) 13th (c) 12th (d) 10th
  17. 17.What is the sum of all the whole numbers from 1 to 65? (a) 2145 (b) 4290 (c) 2146 (d) 2080
  18. 18.Which term of the AP 17, 26, 35, 44, … is 152? (a) 15th (b) 18th (c) 17th (d) 16th
  19. 19.What is the sum of the first 20 odd numbers (1 + 3 + 5 + …)? (a) 400 (b) 210 (c) 420 (d) 39
  20. 20.What is the sum of the first 28 odd numbers (1 + 3 + 5 + …)? (a) 784 (b) 55 (c) 406 (d) 812
  21. 21.Which term of the AP 10, 12, 14, 16, … is 72? (a) 33rd (b) 32nd (c) 36th (d) 31st
  22. 22.What is the missing term in the AP 10, ?, 14, 16, 18? (a) 13 (b) 11 (c) 12 (d) 14
  23. 23.What is the 33rd term of the AP 13, 16, 19, 22, …? (a) 96 (b) 112 (c) 99 (d) 109
  24. 24.What is the sum of all the whole numbers from 1 to 91? (a) 4187 (b) 4095 (c) 4186 (d) 8372
  25. 25.What is the sum of the first 10 terms of the AP 6, 7, 8, …? (a) 15 (b) 105 (c) 210 (d) 110
  26. 26.What is the 28th term of the AP 20, 23, 26, 29, …? (a) 84 (b) 104 (c) 81 (d) 101
  27. 27.What is the sum of all the whole numbers from 1 to 49? (a) 1225 (b) 2450 (c) 1226 (d) 1176
  28. 28.What is the missing term in the AP 6, 9, 12, ?, 18? (a) 15 (b) 14 (c) 18 (d) 16
  29. 29.What is the 38th term of the AP 12, 14, 16, 18, …? (a) 74 (b) 86 (c) 88 (d) 76
  30. 30.What is the sum of the first 12 terms of the AP 1, 3, 5, …? (a) 23 (b) 288 (c) 144 (d) 156
  31. 31.What is the sum of the first 7 terms of the AP 7, 8, 9, …? (a) 13 (b) 71 (c) 140 (d) 70
  32. 32.What is the sum of the first 15 odd numbers (1 + 3 + 5 + …)? (a) 120 (b) 240 (c) 29 (d) 225
  33. 33.What is the 10th term of the AP 9, 14, 19, 24, …? (a) 59 (b) 45 (c) 54 (d) 50
  34. 34.Which term of the AP 10, 18, 26, 34, … is 314? (a) 38th (b) 41st (c) 39th (d) 40th
  35. 35.Which term of the AP 15, 18, 21, 24, … is 54? (a) 18th (b) 15th (c) 14th (d) 13th
  36. 36.What is the sum of the first 12 terms of the AP 6, 11, 16, …? (a) 61 (b) 432 (c) 402 (d) 804
  37. 37.What is the sum of the first 8 terms of the AP 8, 9, 10, …? (a) 184 (b) 92 (c) 15 (d) 96
  38. 38.What is the sum of the first 16 odd numbers (1 + 3 + 5 + …)? (a) 136 (b) 256 (c) 31 (d) 272
  39. 39.What is the sum of the first 27 odd numbers (1 + 3 + 5 + …)? (a) 53 (b) 756 (c) 729 (d) 378
  40. 40.What is the sum of the first 24 odd numbers (1 + 3 + 5 + …)? (a) 47 (b) 576 (c) 600 (d) 300

Answer key

  1. 2278
  2. 242
  3. 95
  4. 441
  5. 143
  6. 78
  7. 156
  8. 27
  9. 18
  10. 126
  11. 99
  12. 12
  13. 49
  14. 251
  15. 47
  16. 11th
  17. 2145
  18. 16th
  19. 400
  20. 784
  21. 32nd
  22. 12
  23. 109
  24. 4186
  25. 105
  26. 101
  27. 1225
  28. 15
  29. 86
  30. 144
  31. 70
  32. 225
  33. 54
  34. 39th
  35. 14th
  36. 402
  37. 92
  38. 256
  39. 729
  40. 576

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