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Arithmetic Progression Worksheet for Olympiad

Maths Olympiad topic 29: Sequences and AP · Set 299 · 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 39? (a) 780 (b) 741 (c) 781 (d) 1560
  2. 2.Which term of the AP 13, 20, 27, 34, … is 146? (a) 22nd (b) 19th (c) 20th (d) 21st
  3. 3.What is the 28th term of the AP 7, 12, 17, 22, …? (a) 135 (b) 140 (c) 142 (d) 147
  4. 4.What is the sum of all the whole numbers from 1 to 30? (a) 435 (b) 450 (c) 465 (d) 930
  5. 5.What is the missing term in the AP 8, ?, 14, 17, 20? (a) 14 (b) 11 (c) 10 (d) 12
  6. 6.What is the 23rd term of the AP 3, 5, 7, 9, …? (a) 46 (b) 49 (c) 44 (d) 47
  7. 7.What is the 12th term of the AP 17, 21, 25, 29, …? (a) 65 (b) 48 (c) 61 (d) 44
  8. 8.Which term of the AP 1, 3, 5, 7, … is 25? (a) 14th (b) 15th (c) 13th (d) 12th
  9. 9.What is the sum of the first 7 odd numbers (1 + 3 + 5 + …)? (a) 49 (b) 28 (c) 56 (d) 13
  10. 10.What is the 10th term of the AP 2, 11, 20, 29, …? (a) 92 (b) 81 (c) 83 (d) 90
  11. 11.What is the 18th term of the AP 10, 15, 20, 25, …? (a) 85 (b) 95 (c) 90 (d) 100
  12. 12.What is the sum of the first 5 terms of the AP 5, 8, 11, …? (a) 58 (b) 17 (c) 110 (d) 55
  13. 13.What is the sum of the first 10 terms of the AP 2, 4, 6, …? (a) 120 (b) 110 (c) 20 (d) 220
  14. 14.What is the 30th term of the AP 2, 11, 20, 29, …? (a) 261 (b) 270 (c) 272 (d) 263
  15. 15.What is the 32nd term of the AP 16, 24, 32, 40, …? (a) 272 (b) 256 (c) 264 (d) 248
  16. 16.What is the sum of the first 27 odd numbers (1 + 3 + 5 + …)? (a) 53 (b) 378 (c) 756 (d) 729
  17. 17.What is the sum of the first 5 terms of the AP 10, 16, 22, …? (a) 110 (b) 220 (c) 125 (d) 34
  18. 18.What is the sum of the first 6 terms of the AP 9, 13, 17, …? (a) 228 (b) 114 (c) 126 (d) 29
  19. 19.What is the sum of all the whole numbers from 1 to 81? (a) 3322 (b) 6642 (c) 3240 (d) 3321
  20. 20.What is the missing term in the AP 13, ?, 31, 40, 49? (a) 23 (b) 21 (c) 31 (d) 22
  21. 21.What is the sum of the first 10 terms of the AP 9, 14, 19, …? (a) 54 (b) 315 (c) 340 (d) 630
  22. 22.What is the sum of the first 7 terms of the AP 6, 12, 18, …? (a) 189 (b) 42 (c) 168 (d) 336
  23. 23.What is the sum of the first 6 terms of the AP 1, 3, 5, …? (a) 42 (b) 72 (c) 36 (d) 11
  24. 24.What is the missing term in the AP 2, 6, ?, 14, 18? (a) 11 (b) 9 (c) 10 (d) 14
  25. 25.What is the 18th term of the AP 8, 14, 20, 26, …? (a) 116 (b) 108 (c) 110 (d) 102
  26. 26.Which term of the AP 18, 23, 28, 33, … is 68? (a) 11th (b) 12th (c) 10th (d) 13th
  27. 27.What is the missing term in the AP 5, 9, ?, 17, 21? (a) 14 (b) 12 (c) 13 (d) 17
  28. 28.What is the sum of the first 11 terms of the AP 8, 9, 10, …? (a) 144 (b) 286 (c) 18 (d) 143
  29. 29.Which term of the AP 3, 7, 11, 15, … is 155? (a) 41st (b) 38th (c) 39th (d) 40th
  30. 30.What is the sum of all the whole numbers from 1 to 71? (a) 2557 (b) 5112 (c) 2556 (d) 2485
  31. 31.What is the sum of the first 5 terms of the AP 6, 10, 14, …? (a) 140 (b) 22 (c) 80 (d) 70
  32. 32.What is the missing term in the AP 8, 12, ?, 20, 24? (a) 16 (b) 15 (c) 17 (d) 20
  33. 33.What is the 21st term of the AP 8, 15, 22, 29, …? (a) 148 (b) 140 (c) 155 (d) 147
  34. 34.Which term of the AP 6, 8, 10, 12, … is 54? (a) 24th (b) 26th (c) 27th (d) 25th
  35. 35.What is the 38th term of the AP 15, 21, 27, 33, …? (a) 243 (b) 228 (c) 222 (d) 237
  36. 36.What is the sum of all the whole numbers from 1 to 22? (a) 231 (b) 506 (c) 242 (d) 253
  37. 37.What is the sum of the first 6 terms of the AP 6, 9, 12, …? (a) 90 (b) 81 (c) 162 (d) 21
  38. 38.What is the sum of the first 7 terms of the AP 4, 5, 6, …? (a) 10 (b) 50 (c) 98 (d) 49
  39. 39.What is the 19th term of the AP 1, 8, 15, 22, …? (a) 134 (b) 133 (c) 126 (d) 127
  40. 40.What is the missing term in the AP 15, ?, 21, 24, 27? (a) 18 (b) 17 (c) 19 (d) 21

Answer key

  1. 780
  2. 20th
  3. 142
  4. 465
  5. 11
  6. 47
  7. 61
  8. 13th
  9. 49
  10. 83
  11. 95
  12. 55
  13. 110
  14. 263
  15. 264
  16. 729
  17. 110
  18. 114
  19. 3321
  20. 22
  21. 315
  22. 168
  23. 36
  24. 10
  25. 110
  26. 11th
  27. 13
  28. 143
  29. 39th
  30. 2556
  31. 70
  32. 16
  33. 148
  34. 25th
  35. 237
  36. 253
  37. 81
  38. 49
  39. 127
  40. 18

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