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Arithmetic Progression Worksheet for Olympiad

Maths Olympiad topic 29: Sequences and AP · Set 867 · 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.Which term of the AP 13, 15, 17, 19, … is 67? (a) 30th (b) 29th (c) 27th (d) 28th
  2. 2.What is the sum of all the whole numbers from 1 to 91? (a) 8372 (b) 4187 (c) 4095 (d) 4186
  3. 3.Which term of the AP 9, 16, 23, 30, … is 184? (a) 26th (b) 25th (c) 27th (d) 28th
  4. 4.What is the 40th term of the AP 19, 22, 25, 28, …? (a) 139 (b) 136 (c) 120 (d) 117
  5. 5.What is the sum of all the whole numbers from 1 to 45? (a) 990 (b) 1036 (c) 1035 (d) 2070
  6. 6.What is the sum of the first 7 terms of the AP 9, 15, 21, …? (a) 210 (b) 45 (c) 189 (d) 378
  7. 7.What is the 12th term of the AP 1, 8, 15, 22, …? (a) 78 (b) 84 (c) 77 (d) 85
  8. 8.What is the sum of all the whole numbers from 1 to 32? (a) 512 (b) 528 (c) 1056 (d) 496
  9. 9.What is the missing term in the AP 18, ?, 24, 27, 30? (a) 24 (b) 21 (c) 20 (d) 22
  10. 10.What is the sum of the first 11 terms of the AP 3, 7, 11, …? (a) 253 (b) 506 (c) 275 (d) 43
  11. 11.What is the sum of the first 10 terms of the AP 7, 11, 15, …? (a) 500 (b) 43 (c) 250 (d) 270
  12. 12.What is the 18th term of the AP 13, 16, 19, 22, …? (a) 67 (b) 54 (c) 64 (d) 51
  13. 13.What is the sum of the first 6 terms of the AP 5, 10, 15, …? (a) 120 (b) 30 (c) 105 (d) 210
  14. 14.What is the sum of the first 12 terms of the AP 3, 8, 13, …? (a) 58 (b) 732 (c) 396 (d) 366
  15. 15.What is the 16th term of the AP 16, 25, 34, 43, …? (a) 135 (b) 144 (c) 160 (d) 151
  16. 16.What is the sum of the first 9 terms of the AP 4, 7, 10, …? (a) 144 (b) 28 (c) 147 (d) 288
  17. 17.Which term of the AP 20, 23, 26, 29, … is 50? (a) 11th (b) 10th (c) 13th (d) 12th
  18. 18.What is the 13th term of the AP 4, 8, 12, 16, …? (a) 56 (b) 48 (c) 52 (d) 53
  19. 19.What is the 24th term of the AP 19, 22, 25, 28, …? (a) 69 (b) 72 (c) 91 (d) 88
  20. 20.What is the 30th term of the AP 2, 9, 16, 23, …? (a) 212 (b) 205 (c) 203 (d) 210
  21. 21.What is the 11th term of the AP 13, 18, 23, 28, …? (a) 55 (b) 68 (c) 50 (d) 63
  22. 22.What is the missing term in the AP 16, ?, 24, 28, 32? (a) 19 (b) 21 (c) 24 (d) 20
  23. 23.What is the sum of the first 12 odd numbers (1 + 3 + 5 + …)? (a) 156 (b) 23 (c) 144 (d) 78
  24. 24.What is the sum of the first 11 odd numbers (1 + 3 + 5 + …)? (a) 66 (b) 132 (c) 121 (d) 21
  25. 25.Which term of the AP 7, 13, 19, 25, … is 235? (a) 41st (b) 38th (c) 40th (d) 39th
  26. 26.Which term of the AP 3, 7, 11, 15, … is 147? (a) 38th (b) 39th (c) 36th (d) 37th
  27. 27.What is the sum of the first 9 odd numbers (1 + 3 + 5 + …)? (a) 90 (b) 45 (c) 17 (d) 81
  28. 28.What is the missing term in the AP 13, 21, 29, ?, 45? (a) 38 (b) 45 (c) 37 (d) 36
  29. 29.What is the missing term in the AP 2, 11, 20, ?, 38? (a) 29 (b) 38 (c) 30 (d) 28
  30. 30.What is the sum of the first 11 terms of the AP 7, 9, 11, …? (a) 198 (b) 374 (c) 187 (d) 27
  31. 31.What is the 31st term of the AP 9, 16, 23, 30, …? (a) 210 (b) 226 (c) 217 (d) 219
  32. 32.What is the sum of the first 11 terms of the AP 9, 13, 17, …? (a) 638 (b) 49 (c) 319 (d) 341
  33. 33.What is the sum of the first 9 terms of the AP 3, 8, 13, …? (a) 212 (b) 207 (c) 414 (d) 43
  34. 34.What is the 15th term of the AP 20, 27, 34, 41, …? (a) 118 (b) 98 (c) 105 (d) 125
  35. 35.What is the missing term in the AP 3, 11, ?, 27, 35? (a) 27 (b) 20 (c) 18 (d) 19
  36. 36.What is the sum of all the whole numbers from 1 to 86? (a) 3698 (b) 7482 (c) 3655 (d) 3741
  37. 37.What is the 25th term of the AP 13, 16, 19, 22, …? (a) 88 (b) 75 (c) 85 (d) 72
  38. 38.What is the 27th term of the AP 9, 14, 19, 24, …? (a) 144 (b) 139 (c) 135 (d) 130
  39. 39.What is the 12th term of the AP 16, 24, 32, 40, …? (a) 96 (b) 112 (c) 104 (d) 88
  40. 40.What is the sum of the first 6 terms of the AP 3, 4, 5, …? (a) 66 (b) 33 (c) 8 (d) 36

Answer key

  1. 28th
  2. 4186
  3. 26th
  4. 136
  5. 1035
  6. 189
  7. 78
  8. 528
  9. 21
  10. 253
  11. 250
  12. 64
  13. 105
  14. 366
  15. 151
  16. 144
  17. 11th
  18. 52
  19. 88
  20. 205
  21. 63
  22. 20
  23. 144
  24. 121
  25. 39th
  26. 37th
  27. 81
  28. 37
  29. 29
  30. 187
  31. 219
  32. 319
  33. 207
  34. 118
  35. 19
  36. 3741
  37. 85
  38. 139
  39. 104
  40. 33

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