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Arithmetic Progression Worksheet for Olympiad

Maths Olympiad topic 29: Sequences and AP · Set 640 · 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 the first 8 terms of the AP 4, 7, 10, …? (a) 25 (b) 128 (c) 232 (d) 116
  2. 2.What is the sum of the first 10 odd numbers (1 + 3 + 5 + …)? (a) 110 (b) 19 (c) 55 (d) 100
  3. 3.What is the 14th term of the AP 5, 9, 13, 17, …? (a) 57 (b) 56 (c) 61 (d) 52
  4. 4.What is the sum of the first 9 odd numbers (1 + 3 + 5 + …)? (a) 45 (b) 81 (c) 90 (d) 17
  5. 5.What is the sum of the first 10 terms of the AP 4, 5, 6, …? (a) 85 (b) 13 (c) 90 (d) 170
  6. 6.What is the missing term in the AP 4, 6, ?, 10, 12? (a) 10 (b) 7 (c) 8 (d) 9
  7. 7.What is the sum of all the whole numbers from 1 to 96? (a) 4608 (b) 4656 (c) 4560 (d) 9312
  8. 8.What is the missing term in the AP 10, 19, ?, 37, 46? (a) 37 (b) 29 (c) 28 (d) 27
  9. 9.What is the 14th term of the AP 6, 15, 24, 33, …? (a) 132 (b) 117 (c) 123 (d) 126
  10. 10.What is the sum of all the whole numbers from 1 to 82? (a) 3362 (b) 3403 (c) 6806 (d) 3321
  11. 11.Which term of the AP 17, 22, 27, 32, … is 97? (a) 16th (b) 18th (c) 17th (d) 19th
  12. 12.What is the sum of the first 12 odd numbers (1 + 3 + 5 + …)? (a) 156 (b) 78 (c) 23 (d) 144
  13. 13.What is the sum of the first 7 terms of the AP 4, 10, 16, …? (a) 40 (b) 308 (c) 175 (d) 154
  14. 14.What is the sum of the first 7 terms of the AP 6, 9, 12, …? (a) 108 (b) 105 (c) 210 (d) 24
  15. 15.Which term of the AP 15, 24, 33, 42, … is 258? (a) 30th (b) 28th (c) 29th (d) 27th
  16. 16.What is the sum of all the whole numbers from 1 to 32? (a) 512 (b) 1056 (c) 528 (d) 496
  17. 17.What is the sum of the first 6 terms of the AP 1, 7, 13, …? (a) 96 (b) 192 (c) 31 (d) 114
  18. 18.What is the 27th term of the AP 6, 14, 22, 30, …? (a) 222 (b) 216 (c) 208 (d) 214
  19. 19.What is the 11th term of the AP 2, 6, 10, 14, …? (a) 44 (b) 40 (c) 46 (d) 42
  20. 20.What is the sum of the first 12 terms of the AP 8, 14, 20, …? (a) 492 (b) 74 (c) 984 (d) 528
  21. 21.What is the 21st term of the AP 8, 11, 14, 17, …? (a) 71 (b) 63 (c) 60 (d) 68
  22. 22.What is the sum of the first 8 terms of the AP 2, 4, 6, …? (a) 144 (b) 72 (c) 16 (d) 80
  23. 23.What is the sum of the first 10 terms of the AP 6, 10, 14, …? (a) 42 (b) 260 (c) 240 (d) 480
  24. 24.What is the missing term in the AP 20, ?, 36, 44, 52? (a) 27 (b) 29 (c) 36 (d) 28
  25. 25.What is the sum of all the whole numbers from 1 to 76? (a) 2850 (b) 2926 (c) 2888 (d) 5852
  26. 26.What is the sum of the first 9 terms of the AP 7, 13, 19, …? (a) 279 (b) 306 (c) 55 (d) 558
  27. 27.What is the missing term in the AP 18, 26, 34, ?, 50? (a) 41 (b) 43 (c) 42 (d) 50
  28. 28.Which term of the AP 14, 21, 28, 35, … is 245? (a) 35th (b) 36th (c) 33rd (d) 34th
  29. 29.What is the sum of all the whole numbers from 1 to 33? (a) 562 (b) 528 (c) 561 (d) 1122
  30. 30.What is the missing term in the AP 14, 20, ?, 32, 38? (a) 27 (b) 26 (c) 32 (d) 25
  31. 31.What is the 24th term of the AP 6, 9, 12, 15, …? (a) 78 (b) 72 (c) 69 (d) 75
  32. 32.What is the 24th term of the AP 1, 8, 15, 22, …? (a) 169 (b) 161 (c) 168 (d) 162
  33. 33.What is the 16th term of the AP 18, 26, 34, 42, …? (a) 146 (b) 120 (c) 138 (d) 128
  34. 34.What is the sum of the first 6 terms of the AP 7, 11, 15, …? (a) 204 (b) 114 (c) 102 (d) 27
  35. 35.What is the sum of the first 10 terms of the AP 4, 6, 8, …? (a) 22 (b) 260 (c) 140 (d) 130
  36. 36.What is the 23rd term of the AP 19, 27, 35, 43, …? (a) 195 (b) 203 (c) 176 (d) 184
  37. 37.What is the sum of the first 8 terms of the AP 6, 8, 10, …? (a) 20 (b) 208 (c) 112 (d) 104
  38. 38.What is the sum of the first 6 terms of the AP 3, 6, 9, …? (a) 126 (b) 72 (c) 18 (d) 63
  39. 39.What is the sum of the first 5 terms of the AP 5, 10, 15, …? (a) 150 (b) 75 (c) 80 (d) 25
  40. 40.What is the sum of all the whole numbers from 1 to 39? (a) 780 (b) 1560 (c) 781 (d) 741

Answer key

  1. 116
  2. 100
  3. 57
  4. 81
  5. 85
  6. 8
  7. 4656
  8. 28
  9. 123
  10. 3403
  11. 17th
  12. 144
  13. 154
  14. 105
  15. 28th
  16. 528
  17. 96
  18. 214
  19. 42
  20. 492
  21. 68
  22. 72
  23. 240
  24. 28
  25. 2926
  26. 279
  27. 42
  28. 34th
  29. 561
  30. 26
  31. 75
  32. 162
  33. 138
  34. 102
  35. 130
  36. 195
  37. 104
  38. 63
  39. 75
  40. 780

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