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Arithmetic Progression Worksheet for Olympiad

Maths Olympiad topic 29: Sequences and AP · Set 839 · 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 68? (a) 2312 (b) 4692 (c) 2278 (d) 2346
  2. 2.What is the missing term in the AP 2, 11, ?, 29, 38? (a) 21 (b) 20 (c) 29 (d) 19
  3. 3.What is the 17th term of the AP 13, 18, 23, 28, …? (a) 98 (b) 80 (c) 93 (d) 85
  4. 4.What is the missing term in the AP 7, 12, 17, ?, 27? (a) 27 (b) 23 (c) 22 (d) 21
  5. 5.What is the sum of the first 6 terms of the AP 4, 10, 16, …? (a) 228 (b) 132 (c) 114 (d) 34
  6. 6.What is the 18th term of the AP 3, 6, 9, 12, …? (a) 51 (b) 55 (c) 54 (d) 57
  7. 7.What is the 35th term of the AP 7, 12, 17, 22, …? (a) 170 (b) 175 (c) 182 (d) 177
  8. 8.What is the 40th term of the AP 20, 23, 26, 29, …? (a) 120 (b) 137 (c) 140 (d) 117
  9. 9.What is the missing term in the AP 3, 9, 15, ?, 27? (a) 27 (b) 20 (c) 22 (d) 21
  10. 10.What is the sum of the first 9 odd numbers (1 + 3 + 5 + …)? (a) 90 (b) 17 (c) 81 (d) 45
  11. 11.What is the sum of the first 17 odd numbers (1 + 3 + 5 + …)? (a) 153 (b) 306 (c) 33 (d) 289
  12. 12.What is the sum of the first 24 odd numbers (1 + 3 + 5 + …)? (a) 300 (b) 47 (c) 600 (d) 576
  13. 13.What is the missing term in the AP 11, ?, 17, 20, 23? (a) 15 (b) 17 (c) 14 (d) 13
  14. 14.Which term of the AP 19, 27, 35, 43, … is 275? (a) 32nd (b) 33rd (c) 35th (d) 34th
  15. 15.What is the sum of the first 12 terms of the AP 8, 13, 18, …? (a) 852 (b) 426 (c) 456 (d) 63
  16. 16.What is the 33rd term of the AP 14, 19, 24, 29, …? (a) 165 (b) 179 (c) 160 (d) 174
  17. 17.What is the missing term in the AP 19, 22, ?, 28, 31? (a) 25 (b) 28 (c) 26 (d) 24
  18. 18.What is the sum of all the whole numbers from 1 to 99? (a) 4851 (b) 4951 (c) 4950 (d) 9900
  19. 19.What is the sum of the first 11 terms of the AP 5, 11, 17, …? (a) 65 (b) 770 (c) 385 (d) 418
  20. 20.What is the sum of all the whole numbers from 1 to 11? (a) 132 (b) 55 (c) 67 (d) 66
  21. 21.Which term of the AP 17, 22, 27, 32, … is 137? (a) 27th (b) 25th (c) 24th (d) 26th
  22. 22.What is the sum of the first 7 terms of the AP 6, 9, 12, …? (a) 105 (b) 210 (c) 24 (d) 108
  23. 23.What is the sum of the first 7 terms of the AP 7, 9, 11, …? (a) 98 (b) 91 (c) 19 (d) 182
  24. 24.What is the 30th term of the AP 19, 28, 37, 46, …? (a) 261 (b) 270 (c) 280 (d) 289
  25. 25.What is the 19th term of the AP 13, 15, 17, 19, …? (a) 36 (b) 51 (c) 38 (d) 49
  26. 26.What is the sum of all the whole numbers from 1 to 13? (a) 91 (b) 92 (c) 182 (d) 78
  27. 27.What is the 12th term of the AP 18, 24, 30, 36, …? (a) 90 (b) 84 (c) 66 (d) 72
  28. 28.What is the missing term in the AP 10, 16, 22, ?, 34? (a) 29 (b) 28 (c) 34 (d) 27
  29. 29.What is the sum of all the whole numbers from 1 to 27? (a) 378 (b) 756 (c) 351 (d) 379
  30. 30.What is the sum of all the whole numbers from 1 to 64? (a) 2016 (b) 4160 (c) 2080 (d) 2048
  31. 31.What is the 27th term of the AP 5, 12, 19, 26, …? (a) 182 (b) 187 (c) 189 (d) 194
  32. 32.What is the missing term in the AP 7, ?, 25, 34, 43? (a) 16 (b) 17 (c) 15 (d) 25
  33. 33.What is the sum of the first 6 terms of the AP 8, 13, 18, …? (a) 33 (b) 138 (c) 123 (d) 246
  34. 34.What is the sum of all the whole numbers from 1 to 17? (a) 306 (b) 136 (c) 153 (d) 154
  35. 35.What is the sum of the first 18 odd numbers (1 + 3 + 5 + …)? (a) 35 (b) 324 (c) 171 (d) 342
  36. 36.Which term of the AP 1, 5, 9, 13, … is 109? (a) 28th (b) 30th (c) 27th (d) 29th
  37. 37.What is the sum of the first 11 terms of the AP 10, 12, 14, …? (a) 440 (b) 30 (c) 220 (d) 231
  38. 38.What is the sum of the first 6 terms of the AP 6, 12, 18, …? (a) 36 (b) 252 (c) 144 (d) 126
  39. 39.What is the sum of the first 5 terms of the AP 5, 6, 7, …? (a) 70 (b) 35 (c) 36 (d) 9
  40. 40.What is the sum of the first 5 terms of the AP 3, 7, 11, …? (a) 55 (b) 19 (c) 110 (d) 65

Answer key

  1. 2346
  2. 20
  3. 93
  4. 22
  5. 114
  6. 54
  7. 177
  8. 137
  9. 21
  10. 81
  11. 289
  12. 576
  13. 14
  14. 33rd
  15. 426
  16. 174
  17. 25
  18. 4950
  19. 385
  20. 66
  21. 25th
  22. 105
  23. 91
  24. 280
  25. 49
  26. 91
  27. 84
  28. 28
  29. 378
  30. 2080
  31. 187
  32. 16
  33. 123
  34. 153
  35. 324
  36. 28th
  37. 220
  38. 126
  39. 35
  40. 55

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