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Arithmetic Progression Worksheet for Olympiad

Maths Olympiad topic 29: Sequences and AP · Set 876 · 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 31? (a) 496 (b) 992 (c) 497 (d) 465
  2. 2.What is the missing term in the AP 1, 6, 11, ?, 21? (a) 21 (b) 17 (c) 16 (d) 15
  3. 3.What is the sum of the first 12 terms of the AP 5, 9, 13, …? (a) 49 (b) 324 (c) 348 (d) 648
  4. 4.What is the 10th term of the AP 1, 7, 13, 19, …? (a) 61 (b) 54 (c) 55 (d) 60
  5. 5.What is the 13th term of the AP 11, 13, 15, 17, …? (a) 24 (b) 37 (c) 35 (d) 26
  6. 6.What is the sum of the first 23 odd numbers (1 + 3 + 5 + …)? (a) 276 (b) 45 (c) 529 (d) 552
  7. 7.What is the missing term in the AP 18, ?, 26, 30, 34? (a) 21 (b) 26 (c) 23 (d) 22
  8. 8.What is the sum of the first 11 terms of the AP 8, 12, 16, …? (a) 330 (b) 48 (c) 308 (d) 616
  9. 9.What is the sum of the first 6 terms of the AP 6, 12, 18, …? (a) 252 (b) 144 (c) 126 (d) 36
  10. 10.What is the sum of all the whole numbers from 1 to 45? (a) 2070 (b) 1036 (c) 1035 (d) 990
  11. 11.What is the sum of all the whole numbers from 1 to 61? (a) 3782 (b) 1892 (c) 1891 (d) 1830
  12. 12.What is the sum of the first 7 terms of the AP 7, 13, 19, …? (a) 43 (b) 175 (c) 196 (d) 350
  13. 13.What is the sum of all the whole numbers from 1 to 24? (a) 288 (b) 300 (c) 600 (d) 276
  14. 14.What is the missing term in the AP 12, 15, 18, ?, 24? (a) 22 (b) 21 (c) 20 (d) 24
  15. 15.What is the 31st term of the AP 10, 19, 28, 37, …? (a) 279 (b) 270 (c) 280 (d) 289
  16. 16.What is the missing term in the AP 3, ?, 11, 15, 19? (a) 6 (b) 11 (c) 7 (d) 8
  17. 17.What is the 40th term of the AP 8, 17, 26, 35, …? (a) 368 (b) 351 (c) 360 (d) 359
  18. 18.What is the missing term in the AP 4, 9, 14, ?, 24? (a) 18 (b) 24 (c) 19 (d) 20
  19. 19.What is the 33rd term of the AP 16, 18, 20, 22, …? (a) 82 (b) 80 (c) 66 (d) 64
  20. 20.What is the sum of the first 8 terms of the AP 7, 10, 13, …? (a) 140 (b) 28 (c) 152 (d) 280
  21. 21.What is the missing term in the AP 16, 22, 28, ?, 40? (a) 33 (b) 40 (c) 35 (d) 34
  22. 22.What is the missing term in the AP 4, ?, 10, 13, 16? (a) 10 (b) 7 (c) 8 (d) 6
  23. 23.What is the missing term in the AP 10, 13, ?, 19, 22? (a) 19 (b) 15 (c) 16 (d) 17
  24. 24.Which term of the AP 6, 13, 20, 27, … is 118? (a) 18th (b) 19th (c) 17th (d) 16th
  25. 25.What is the sum of the first 7 terms of the AP 7, 11, 15, …? (a) 266 (b) 31 (c) 147 (d) 133
  26. 26.What is the sum of the first 5 odd numbers (1 + 3 + 5 + …)? (a) 15 (b) 9 (c) 25 (d) 30
  27. 27.What is the sum of all the whole numbers from 1 to 66? (a) 2211 (b) 2178 (c) 2145 (d) 4422
  28. 28.What is the sum of the first 21 odd numbers (1 + 3 + 5 + …)? (a) 41 (b) 462 (c) 231 (d) 441
  29. 29.What is the sum of the first 11 terms of the AP 1, 3, 5, …? (a) 132 (b) 121 (c) 21 (d) 242
  30. 30.What is the sum of all the whole numbers from 1 to 97? (a) 4754 (b) 4656 (c) 9506 (d) 4753
  31. 31.What is the sum of the first 7 terms of the AP 3, 4, 5, …? (a) 43 (b) 42 (c) 84 (d) 9
  32. 32.What is the sum of the first 9 terms of the AP 7, 13, 19, …? (a) 55 (b) 279 (c) 306 (d) 558
  33. 33.What is the 30th term of the AP 2, 9, 16, 23, …? (a) 210 (b) 212 (c) 203 (d) 205
  34. 34.What is the sum of the first 12 terms of the AP 2, 8, 14, …? (a) 840 (b) 420 (c) 456 (d) 68
  35. 35.What is the sum of the first 6 terms of the AP 9, 12, 15, …? (a) 198 (b) 108 (c) 24 (d) 99
  36. 36.What is the missing term in the AP 15, 20, 25, ?, 35? (a) 29 (b) 30 (c) 35 (d) 31
  37. 37.What is the sum of the first 17 odd numbers (1 + 3 + 5 + …)? (a) 289 (b) 153 (c) 306 (d) 33
  38. 38.What is the sum of all the whole numbers from 1 to 85? (a) 7310 (b) 3655 (c) 3570 (d) 3656
  39. 39.What is the sum of the first 8 terms of the AP 1, 6, 11, …? (a) 168 (b) 148 (c) 36 (d) 296
  40. 40.What is the missing term in the AP 4, 13, 22, ?, 40? (a) 31 (b) 32 (c) 40 (d) 30

Answer key

  1. 496
  2. 16
  3. 324
  4. 55
  5. 35
  6. 529
  7. 22
  8. 308
  9. 126
  10. 1035
  11. 1891
  12. 175
  13. 300
  14. 21
  15. 280
  16. 7
  17. 359
  18. 19
  19. 80
  20. 140
  21. 34
  22. 7
  23. 16
  24. 17th
  25. 133
  26. 25
  27. 2211
  28. 441
  29. 121
  30. 4753
  31. 42
  32. 279
  33. 205
  34. 420
  35. 99
  36. 30
  37. 289
  38. 3655
  39. 148
  40. 31

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