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Arithmetic Progression Worksheet for Olympiad

Maths Olympiad topic 29: Sequences and AP · Set 654 · 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 6 terms of the AP 4, 8, 12, …? (a) 168 (b) 84 (c) 96 (d) 24
  2. 2.Which term of the AP 18, 21, 24, 27, … is 84? (a) 23rd (b) 28th (c) 22nd (d) 24th
  3. 3.Which term of the AP 19, 24, 29, 34, … is 109? (a) 18th (b) 20th (c) 19th (d) 21st
  4. 4.What is the sum of all the whole numbers from 1 to 46? (a) 1058 (b) 2162 (c) 1081 (d) 1035
  5. 5.What is the sum of all the whole numbers from 1 to 65? (a) 2080 (b) 4290 (c) 2145 (d) 2146
  6. 6.What is the sum of the first 27 odd numbers (1 + 3 + 5 + …)? (a) 53 (b) 756 (c) 378 (d) 729
  7. 7.What is the sum of the first 13 odd numbers (1 + 3 + 5 + …)? (a) 182 (b) 169 (c) 25 (d) 91
  8. 8.What is the missing term in the AP 9, ?, 23, 30, 37? (a) 17 (b) 23 (c) 16 (d) 15
  9. 9.What is the sum of all the whole numbers from 1 to 69? (a) 2415 (b) 4830 (c) 2416 (d) 2346
  10. 10.What is the sum of the first 19 odd numbers (1 + 3 + 5 + …)? (a) 190 (b) 361 (c) 37 (d) 380
  11. 11.What is the sum of the first 5 terms of the AP 10, 11, 12, …? (a) 120 (b) 60 (c) 14 (d) 61
  12. 12.What is the 19th term of the AP 7, 11, 15, 19, …? (a) 72 (b) 79 (c) 76 (d) 83
  13. 13.What is the sum of the first 6 terms of the AP 2, 8, 14, …? (a) 204 (b) 102 (c) 120 (d) 32
  14. 14.What is the sum of the first 5 terms of the AP 4, 7, 10, …? (a) 100 (b) 53 (c) 50 (d) 16
  15. 15.What is the missing term in the AP 1, 7, 13, ?, 25? (a) 19 (b) 20 (c) 25 (d) 18
  16. 16.What is the 18th term of the AP 12, 21, 30, 39, …? (a) 174 (b) 153 (c) 165 (d) 162
  17. 17.What is the sum of all the whole numbers from 1 to 35? (a) 630 (b) 595 (c) 1260 (d) 631
  18. 18.What is the 34th term of the AP 9, 15, 21, 27, …? (a) 213 (b) 204 (c) 207 (d) 198
  19. 19.Which term of the AP 12, 15, 18, 21, … is 42? (a) 11th (b) 10th (c) 14th (d) 12th
  20. 20.What is the 13th term of the AP 16, 18, 20, 22, …? (a) 40 (b) 42 (c) 26 (d) 24
  21. 21.Which term of the AP 20, 28, 36, 44, … is 204? (a) 23rd (b) 26th (c) 25th (d) 24th
  22. 22.What is the sum of all the whole numbers from 1 to 52? (a) 1326 (b) 1352 (c) 2756 (d) 1378
  23. 23.What is the sum of the first 6 terms of the AP 7, 13, 19, …? (a) 264 (b) 132 (c) 150 (d) 37
  24. 24.What is the missing term in the AP 20, 24, ?, 32, 36? (a) 29 (b) 32 (c) 27 (d) 28
  25. 25.What is the sum of all the whole numbers from 1 to 85? (a) 3656 (b) 7310 (c) 3570 (d) 3655
  26. 26.Which term of the AP 7, 9, 11, 13, … is 59? (a) 26th (b) 29th (c) 27th (d) 28th
  27. 27.Which term of the AP 9, 13, 17, 21, … is 125? (a) 32nd (b) 31st (c) 30th (d) 29th
  28. 28.What is the sum of the first 11 terms of the AP 10, 13, 16, …? (a) 40 (b) 550 (c) 275 (d) 278
  29. 29.What is the 12th term of the AP 15, 23, 31, 39, …? (a) 88 (b) 96 (c) 103 (d) 111
  30. 30.What is the sum of all the whole numbers from 1 to 22? (a) 253 (b) 242 (c) 231 (d) 506
  31. 31.What is the 33rd term of the AP 15, 20, 25, 30, …? (a) 180 (b) 160 (c) 175 (d) 165
  32. 32.What is the sum of all the whole numbers from 1 to 37? (a) 666 (b) 703 (c) 704 (d) 1406
  33. 33.What is the sum of the first 5 terms of the AP 10, 15, 20, …? (a) 200 (b) 105 (c) 100 (d) 30
  34. 34.What is the 14th term of the AP 20, 23, 26, 29, …? (a) 42 (b) 62 (c) 39 (d) 59
  35. 35.What is the 37th term of the AP 7, 12, 17, 22, …? (a) 187 (b) 192 (c) 180 (d) 185
  36. 36.What is the 15th term of the AP 18, 23, 28, 33, …? (a) 88 (b) 75 (c) 93 (d) 70
  37. 37.What is the sum of the first 7 terms of the AP 8, 9, 10, …? (a) 154 (b) 78 (c) 77 (d) 14
  38. 38.What is the 11th term of the AP 6, 9, 12, 15, …? (a) 33 (b) 36 (c) 39 (d) 30
  39. 39.What is the sum of the first 5 terms of the AP 9, 13, 17, …? (a) 170 (b) 85 (c) 25 (d) 95
  40. 40.What is the sum of the first 22 odd numbers (1 + 3 + 5 + …)? (a) 506 (b) 484 (c) 43 (d) 253

Answer key

  1. 84
  2. 23rd
  3. 19th
  4. 1081
  5. 2145
  6. 729
  7. 169
  8. 16
  9. 2415
  10. 361
  11. 60
  12. 79
  13. 102
  14. 50
  15. 19
  16. 165
  17. 630
  18. 207
  19. 11th
  20. 40
  21. 24th
  22. 1378
  23. 132
  24. 28
  25. 3655
  26. 27th
  27. 30th
  28. 275
  29. 103
  30. 253
  31. 175
  32. 703
  33. 100
  34. 59
  35. 187
  36. 88
  37. 77
  38. 36
  39. 85
  40. 484

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