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Arithmetic Progression Worksheet for Olympiad

Maths Olympiad topic 29: Sequences and AP · Set 721 · 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 15 odd numbers (1 + 3 + 5 + …)? (a) 29 (b) 225 (c) 120 (d) 240
  2. 2.What is the sum of the first 10 terms of the AP 1, 3, 5, …? (a) 110 (b) 200 (c) 100 (d) 19
  3. 3.Which term of the AP 8, 14, 20, 26, … is 146? (a) 26th (b) 24th (c) 23rd (d) 25th
  4. 4.What is the missing term in the AP 7, 13, ?, 25, 31? (a) 18 (b) 19 (c) 25 (d) 20
  5. 5.What is the sum of all the whole numbers from 1 to 74? (a) 2701 (b) 5550 (c) 2738 (d) 2775
  6. 6.What is the sum of the first 6 terms of the AP 3, 9, 15, …? (a) 216 (b) 126 (c) 108 (d) 33
  7. 7.What is the sum of all the whole numbers from 1 to 68? (a) 2346 (b) 4692 (c) 2312 (d) 2278
  8. 8.What is the 36th term of the AP 10, 12, 14, 16, …? (a) 72 (b) 70 (c) 80 (d) 82
  9. 9.What is the 14th term of the AP 20, 22, 24, 26, …? (a) 28 (b) 48 (c) 26 (d) 46
  10. 10.What is the sum of the first 10 terms of the AP 4, 7, 10, …? (a) 350 (b) 31 (c) 190 (d) 175
  11. 11.What is the missing term in the AP 11, 17, ?, 29, 35? (a) 29 (b) 23 (c) 22 (d) 24
  12. 12.What is the missing term in the AP 10, ?, 16, 19, 22? (a) 12 (b) 16 (c) 13 (d) 14
  13. 13.What is the 28th term of the AP 2, 7, 12, 17, …? (a) 142 (b) 135 (c) 137 (d) 140
  14. 14.What is the missing term in the AP 2, 8, 14, ?, 26? (a) 19 (b) 20 (c) 21 (d) 26
  15. 15.What is the sum of the first 18 odd numbers (1 + 3 + 5 + …)? (a) 171 (b) 324 (c) 35 (d) 342
  16. 16.What is the sum of the first 10 terms of the AP 7, 9, 11, …? (a) 170 (b) 320 (c) 25 (d) 160
  17. 17.What is the sum of all the whole numbers from 1 to 52? (a) 2756 (b) 1326 (c) 1352 (d) 1378
  18. 18.What is the sum of all the whole numbers from 1 to 77? (a) 3004 (b) 2926 (c) 3003 (d) 6006
  19. 19.What is the 17th term of the AP 13, 19, 25, 31, …? (a) 115 (b) 102 (c) 109 (d) 96
  20. 20.What is the sum of the first 11 terms of the AP 2, 8, 14, …? (a) 352 (b) 385 (c) 62 (d) 704
  21. 21.What is the 17th term of the AP 10, 14, 18, 22, …? (a) 64 (b) 78 (c) 68 (d) 74
  22. 22.What is the sum of all the whole numbers from 1 to 57? (a) 1653 (b) 1654 (c) 3306 (d) 1596
  23. 23.What is the sum of the first 10 terms of the AP 4, 6, 8, …? (a) 22 (b) 130 (c) 140 (d) 260
  24. 24.Which term of the AP 20, 27, 34, 41, … is 132? (a) 19th (b) 16th (c) 17th (d) 18th
  25. 25.What is the sum of all the whole numbers from 1 to 38? (a) 1482 (b) 741 (c) 703 (d) 722
  26. 26.What is the 22nd term of the AP 14, 18, 22, 26, …? (a) 84 (b) 98 (c) 88 (d) 102
  27. 27.What is the missing term in the AP 16, 23, ?, 37, 44? (a) 30 (b) 37 (c) 29 (d) 31
  28. 28.What is the 11th term of the AP 5, 12, 19, 26, …? (a) 70 (b) 82 (c) 77 (d) 75
  29. 29.Which term of the AP 2, 8, 14, 20, … is 98? (a) 16th (b) 18th (c) 17th (d) 19th
  30. 30.What is the 32nd term of the AP 1, 10, 19, 28, …? (a) 289 (b) 279 (c) 280 (d) 288
  31. 31.What is the sum of all the whole numbers from 1 to 19? (a) 191 (b) 380 (c) 171 (d) 190
  32. 32.What is the sum of the first 10 terms of the AP 10, 11, 12, …? (a) 290 (b) 19 (c) 145 (d) 150
  33. 33.What is the sum of all the whole numbers from 1 to 49? (a) 2450 (b) 1226 (c) 1176 (d) 1225
  34. 34.What is the sum of the first 11 terms of the AP 2, 7, 12, …? (a) 52 (b) 297 (c) 594 (d) 302
  35. 35.What is the sum of all the whole numbers from 1 to 86? (a) 3698 (b) 3655 (c) 7482 (d) 3741
  36. 36.Which term of the AP 17, 20, 23, 26, … is 38? (a) 8th (b) 10th (c) 7th (d) 9th
  37. 37.What is the sum of the first 12 terms of the AP 2, 4, 6, …? (a) 312 (b) 156 (c) 168 (d) 24
  38. 38.What is the sum of the first 5 terms of the AP 3, 5, 7, …? (a) 11 (b) 40 (c) 70 (d) 35
  39. 39.Which term of the AP 6, 13, 20, 27, … is 230? (a) 33rd (b) 35th (c) 34th (d) 32nd
  40. 40.What is the sum of all the whole numbers from 1 to 62? (a) 1922 (b) 1953 (c) 3906 (d) 1891

Answer key

  1. 225
  2. 100
  3. 24th
  4. 19
  5. 2775
  6. 108
  7. 2346
  8. 80
  9. 46
  10. 175
  11. 23
  12. 13
  13. 137
  14. 20
  15. 324
  16. 160
  17. 1378
  18. 3003
  19. 109
  20. 352
  21. 74
  22. 1653
  23. 130
  24. 17th
  25. 741
  26. 98
  27. 30
  28. 75
  29. 17th
  30. 280
  31. 190
  32. 145
  33. 1225
  34. 297
  35. 3741
  36. 8th
  37. 156
  38. 35
  39. 33rd
  40. 1953

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