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Arithmetic Progression Worksheet for Olympiad

Maths Olympiad topic 29: Sequences and AP · Set 23 · 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 19, 26, 33, 40, … is 229? (a) 32nd (b) 31st (c) 30th (d) 33rd
  2. 2.What is the sum of all the whole numbers from 1 to 62? (a) 1953 (b) 1922 (c) 3906 (d) 1891
  3. 3.Which term of the AP 3, 8, 13, 18, … is 138? (a) 28th (b) 29th (c) 27th (d) 30th
  4. 4.What is the 30th term of the AP 15, 20, 25, 30, …? (a) 150 (b) 165 (c) 145 (d) 160
  5. 5.What is the sum of the first 12 terms of the AP 7, 13, 19, …? (a) 73 (b) 480 (c) 516 (d) 960
  6. 6.Which term of the AP 6, 9, 12, 15, … is 36? (a) 12th (b) 10th (c) 11th (d) 13th
  7. 7.What is the sum of the first 5 terms of the AP 8, 14, 20, …? (a) 115 (b) 200 (c) 32 (d) 100
  8. 8.What is the sum of all the whole numbers from 1 to 31? (a) 465 (b) 497 (c) 992 (d) 496
  9. 9.What is the 21st term of the AP 19, 25, 31, 37, …? (a) 139 (b) 126 (c) 120 (d) 145
  10. 10.Which term of the AP 1, 6, 11, 16, … is 61? (a) 13th (b) 12th (c) 15th (d) 14th
  11. 11.What is the sum of all the whole numbers from 1 to 27? (a) 756 (b) 379 (c) 351 (d) 378
  12. 12.What is the sum of the first 16 odd numbers (1 + 3 + 5 + …)? (a) 136 (b) 272 (c) 31 (d) 256
  13. 13.What is the 24th term of the AP 19, 22, 25, 28, …? (a) 72 (b) 91 (c) 88 (d) 69
  14. 14.What is the sum of all the whole numbers from 1 to 66? (a) 2178 (b) 4422 (c) 2211 (d) 2145
  15. 15.What is the sum of all the whole numbers from 1 to 70? (a) 2485 (b) 4970 (c) 2450 (d) 2415
  16. 16.Which term of the AP 11, 17, 23, 29, … is 77? (a) 13th (b) 11th (c) 14th (d) 12th
  17. 17.Which term of the AP 9, 11, 13, 15, … is 81? (a) 38th (b) 39th (c) 36th (d) 37th
  18. 18.What is the missing term in the AP 20, 25, ?, 35, 40? (a) 31 (b) 35 (c) 29 (d) 30
  19. 19.What is the sum of the first 24 odd numbers (1 + 3 + 5 + …)? (a) 600 (b) 576 (c) 47 (d) 300
  20. 20.What is the sum of all the whole numbers from 1 to 18? (a) 153 (b) 162 (c) 342 (d) 171
  21. 21.What is the sum of the first 15 odd numbers (1 + 3 + 5 + …)? (a) 29 (b) 225 (c) 120 (d) 240
  22. 22.What is the sum of all the whole numbers from 1 to 17? (a) 306 (b) 153 (c) 136 (d) 154
  23. 23.What is the sum of all the whole numbers from 1 to 67? (a) 4556 (b) 2279 (c) 2211 (d) 2278
  24. 24.Which term of the AP 16, 22, 28, 34, … is 250? (a) 39th (b) 41st (c) 42nd (d) 40th
  25. 25.Which term of the AP 3, 10, 17, 24, … is 52? (a) 7th (b) 9th (c) 10th (d) 8th
  26. 26.What is the 30th term of the AP 19, 27, 35, 43, …? (a) 240 (b) 232 (c) 251 (d) 259
  27. 27.What is the sum of the first 7 terms of the AP 2, 6, 10, …? (a) 26 (b) 196 (c) 98 (d) 112
  28. 28.Which term of the AP 18, 22, 26, 30, … is 58? (a) 12th (b) 11th (c) 10th (d) 13th
  29. 29.What is the 20th term of the AP 2, 9, 16, 23, …? (a) 133 (b) 140 (c) 142 (d) 135
  30. 30.What is the sum of the first 5 terms of the AP 3, 5, 7, …? (a) 70 (b) 11 (c) 40 (d) 35
  31. 31.What is the missing term in the AP 6, 12, ?, 24, 30? (a) 18 (b) 17 (c) 19 (d) 24
  32. 32.What is the sum of all the whole numbers from 1 to 76? (a) 2850 (b) 2926 (c) 5852 (d) 2888
  33. 33.What is the sum of all the whole numbers from 1 to 40? (a) 820 (b) 1640 (c) 780 (d) 800
  34. 34.What is the 16th term of the AP 2, 10, 18, 26, …? (a) 120 (b) 130 (c) 128 (d) 122
  35. 35.What is the 29th term of the AP 20, 28, 36, 44, …? (a) 252 (b) 224 (c) 244 (d) 232
  36. 36.What is the sum of all the whole numbers from 1 to 57? (a) 3306 (b) 1596 (c) 1654 (d) 1653
  37. 37.What is the 13th term of the AP 1, 4, 7, 10, …? (a) 39 (b) 36 (c) 40 (d) 37
  38. 38.What is the sum of the first 6 terms of the AP 8, 9, 10, …? (a) 126 (b) 66 (c) 63 (d) 13
  39. 39.What is the missing term in the AP 5, ?, 11, 14, 17? (a) 7 (b) 9 (c) 11 (d) 8
  40. 40.What is the sum of the first 12 terms of the AP 5, 10, 15, …? (a) 390 (b) 420 (c) 60 (d) 780

Answer key

  1. 31st
  2. 1953
  3. 28th
  4. 160
  5. 480
  6. 11th
  7. 100
  8. 496
  9. 139
  10. 13th
  11. 378
  12. 256
  13. 88
  14. 2211
  15. 2485
  16. 12th
  17. 37th
  18. 30
  19. 576
  20. 171
  21. 225
  22. 153
  23. 2278
  24. 40th
  25. 8th
  26. 251
  27. 98
  28. 11th
  29. 135
  30. 35
  31. 18
  32. 2926
  33. 820
  34. 122
  35. 244
  36. 1653
  37. 37
  38. 63
  39. 8
  40. 390

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