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Arithmetic Progression Worksheet for Olympiad

Maths Olympiad topic 29: Sequences and AP · Set 188 · 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 39th term of the AP 3, 11, 19, 27, …? (a) 315 (b) 312 (c) 307 (d) 304
  2. 2.What is the sum of all the whole numbers from 1 to 39? (a) 780 (b) 741 (c) 781 (d) 1560
  3. 3.What is the sum of the first 5 terms of the AP 6, 8, 10, …? (a) 100 (b) 55 (c) 50 (d) 14
  4. 4.What is the sum of all the whole numbers from 1 to 71? (a) 5112 (b) 2485 (c) 2557 (d) 2556
  5. 5.What is the sum of all the whole numbers from 1 to 17? (a) 306 (b) 153 (c) 136 (d) 154
  6. 6.What is the 27th term of the AP 7, 10, 13, 16, …? (a) 88 (b) 85 (c) 78 (d) 81
  7. 7.What is the 15th term of the AP 9, 14, 19, 24, …? (a) 70 (b) 75 (c) 79 (d) 84
  8. 8.What is the missing term in the AP 12, 16, 20, ?, 28? (a) 24 (b) 25 (c) 23 (d) 28
  9. 9.What is the 12th term of the AP 1, 4, 7, 10, …? (a) 33 (b) 36 (c) 37 (d) 34
  10. 10.What is the sum of all the whole numbers from 1 to 69? (a) 2415 (b) 2346 (c) 2416 (d) 4830
  11. 11.What is the sum of all the whole numbers from 1 to 14? (a) 91 (b) 98 (c) 210 (d) 105
  12. 12.What is the 21st term of the AP 16, 20, 24, 28, …? (a) 80 (b) 84 (c) 96 (d) 100
  13. 13.What is the 13th term of the AP 7, 11, 15, 19, …? (a) 52 (b) 59 (c) 48 (d) 55
  14. 14.What is the sum of the first 5 terms of the AP 1, 3, 5, …? (a) 50 (b) 9 (c) 30 (d) 25
  15. 15.What is the sum of the first 7 terms of the AP 1, 5, 9, …? (a) 182 (b) 25 (c) 91 (d) 105
  16. 16.What is the sum of the first 7 terms of the AP 3, 5, 7, …? (a) 70 (b) 15 (c) 126 (d) 63
  17. 17.What is the sum of the first 6 terms of the AP 5, 7, 9, …? (a) 15 (b) 66 (c) 120 (d) 60
  18. 18.What is the 33rd term of the AP 10, 17, 24, 31, …? (a) 224 (b) 231 (c) 234 (d) 241
  19. 19.What is the sum of all the whole numbers from 1 to 34? (a) 561 (b) 578 (c) 595 (d) 1190
  20. 20.What is the missing term in the AP 19, 21, 23, ?, 27? (a) 24 (b) 26 (c) 25 (d) 27
  21. 21.What is the 10th term of the AP 8, 10, 12, 14, …? (a) 28 (b) 20 (c) 18 (d) 26
  22. 22.What is the missing term in the AP 1, 10, ?, 28, 37? (a) 20 (b) 19 (c) 28 (d) 18
  23. 23.What is the sum of all the whole numbers from 1 to 43? (a) 1892 (b) 947 (c) 946 (d) 903
  24. 24.What is the sum of the first 7 terms of the AP 3, 4, 5, …? (a) 43 (b) 42 (c) 84 (d) 9
  25. 25.What is the missing term in the AP 14, 19, 24, ?, 34? (a) 30 (b) 28 (c) 34 (d) 29
  26. 26.What is the sum of the first 6 terms of the AP 3, 9, 15, …? (a) 126 (b) 216 (c) 33 (d) 108
  27. 27.What is the sum of the first 28 odd numbers (1 + 3 + 5 + …)? (a) 55 (b) 406 (c) 784 (d) 812
  28. 28.What is the sum of the first 10 terms of the AP 9, 10, 11, …? (a) 135 (b) 18 (c) 140 (d) 270
  29. 29.What is the sum of the first 24 odd numbers (1 + 3 + 5 + …)? (a) 47 (b) 576 (c) 300 (d) 600
  30. 30.What is the sum of the first 5 terms of the AP 1, 2, 3, …? (a) 16 (b) 5 (c) 15 (d) 30
  31. 31.What is the sum of the first 14 odd numbers (1 + 3 + 5 + …)? (a) 105 (b) 210 (c) 27 (d) 196
  32. 32.What is the 34th term of the AP 6, 8, 10, 12, …? (a) 66 (b) 74 (c) 72 (d) 68
  33. 33.Which term of the AP 4, 6, 8, 10, … is 76? (a) 37th (b) 39th (c) 38th (d) 36th
  34. 34.What is the 15th term of the AP 4, 7, 10, 13, …? (a) 45 (b) 46 (c) 42 (d) 49
  35. 35.What is the 26th term of the AP 20, 25, 30, 35, …? (a) 145 (b) 125 (c) 150 (d) 130
  36. 36.What is the sum of the first 5 terms of the AP 2, 3, 4, …? (a) 20 (b) 40 (c) 21 (d) 6
  37. 37.What is the sum of the first 21 odd numbers (1 + 3 + 5 + …)? (a) 41 (b) 231 (c) 462 (d) 441
  38. 38.What is the missing term in the AP 8, 15, 22, ?, 36? (a) 30 (b) 29 (c) 36 (d) 28
  39. 39.What is the sum of the first 8 terms of the AP 1, 2, 3, …? (a) 72 (b) 40 (c) 8 (d) 36
  40. 40.What is the 25th term of the AP 19, 27, 35, 43, …? (a) 211 (b) 200 (c) 192 (d) 219

Answer key

  1. 307
  2. 780
  3. 50
  4. 2556
  5. 153
  6. 85
  7. 79
  8. 24
  9. 34
  10. 2415
  11. 105
  12. 96
  13. 55
  14. 25
  15. 91
  16. 63
  17. 60
  18. 234
  19. 595
  20. 25
  21. 26
  22. 19
  23. 946
  24. 42
  25. 29
  26. 108
  27. 784
  28. 135
  29. 576
  30. 15
  31. 196
  32. 72
  33. 37th
  34. 46
  35. 145
  36. 20
  37. 441
  38. 29
  39. 36
  40. 211

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