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Arithmetic Progression Worksheet for Olympiad

Maths Olympiad topic 29: Sequences and AP · Set 758 · 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 9 terms of the AP 9, 15, 21, …? (a) 594 (b) 57 (c) 297 (d) 324
  2. 2.What is the missing term in the AP 9, ?, 17, 21, 25? (a) 12 (b) 13 (c) 14 (d) 17
  3. 3.What is the 25th term of the AP 15, 17, 19, 21, …? (a) 50 (b) 48 (c) 63 (d) 65
  4. 4.What is the sum of the first 12 terms of the AP 7, 13, 19, …? (a) 960 (b) 480 (c) 73 (d) 516
  5. 5.Which term of the AP 2, 5, 8, 11, … is 95? (a) 32nd (b) 34th (c) 33rd (d) 31st
  6. 6.Which term of the AP 13, 15, 17, 19, … is 81? (a) 35th (b) 36th (c) 34th (d) 37th
  7. 7.What is the sum of the first 5 terms of the AP 9, 14, 19, …? (a) 100 (b) 95 (c) 29 (d) 190
  8. 8.What is the sum of all the whole numbers from 1 to 99? (a) 9900 (b) 4950 (c) 4951 (d) 4851
  9. 9.What is the missing term in the AP 17, 24, ?, 38, 45? (a) 30 (b) 38 (c) 32 (d) 31
  10. 10.What is the sum of all the whole numbers from 1 to 85? (a) 3656 (b) 7310 (c) 3655 (d) 3570
  11. 11.What is the sum of the first 10 terms of the AP 8, 10, 12, …? (a) 180 (b) 340 (c) 170 (d) 26
  12. 12.What is the missing term in the AP 3, ?, 19, 27, 35? (a) 19 (b) 12 (c) 11 (d) 10
  13. 13.What is the 13th term of the AP 11, 15, 19, 23, …? (a) 59 (b) 63 (c) 48 (d) 52
  14. 14.Which term of the AP 6, 12, 18, 24, … is 174? (a) 30th (b) 29th (c) 28th (d) 31st
  15. 15.Which term of the AP 10, 17, 24, 31, … is 206? (a) 30th (b) 28th (c) 29th (d) 31st
  16. 16.What is the sum of the first 12 terms of the AP 2, 5, 8, …? (a) 240 (b) 222 (c) 35 (d) 444
  17. 17.What is the sum of the first 23 odd numbers (1 + 3 + 5 + …)? (a) 276 (b) 45 (c) 552 (d) 529
  18. 18.What is the 13th term of the AP 6, 10, 14, 18, …? (a) 54 (b) 58 (c) 52 (d) 48
  19. 19.What is the missing term in the AP 18, 27, 36, ?, 54? (a) 54 (b) 46 (c) 44 (d) 45
  20. 20.Which term of the AP 3, 9, 15, 21, … is 111? (a) 18th (b) 20th (c) 19th (d) 21st
  21. 21.What is the 14th term of the AP 17, 19, 21, 23, …? (a) 43 (b) 45 (c) 26 (d) 28
  22. 22.Which term of the AP 20, 23, 26, 29, … is 125? (a) 36th (b) 37th (c) 38th (d) 35th
  23. 23.What is the sum of all the whole numbers from 1 to 80? (a) 3240 (b) 3200 (c) 3160 (d) 6480
  24. 24.What is the sum of the first 12 terms of the AP 3, 7, 11, …? (a) 47 (b) 324 (c) 600 (d) 300
  25. 25.What is the sum of all the whole numbers from 1 to 78? (a) 6162 (b) 3081 (c) 3042 (d) 3003
  26. 26.What is the sum of all the whole numbers from 1 to 61? (a) 1830 (b) 3782 (c) 1892 (d) 1891
  27. 27.What is the sum of the first 6 odd numbers (1 + 3 + 5 + …)? (a) 21 (b) 11 (c) 42 (d) 36
  28. 28.What is the sum of all the whole numbers from 1 to 12? (a) 66 (b) 72 (c) 156 (d) 78
  29. 29.What is the 19th term of the AP 8, 16, 24, 32, …? (a) 153 (b) 152 (c) 144 (d) 160
  30. 30.What is the 27th term of the AP 3, 12, 21, 30, …? (a) 237 (b) 246 (c) 234 (d) 243
  31. 31.What is the sum of all the whole numbers from 1 to 63? (a) 4032 (b) 2017 (c) 2016 (d) 1953
  32. 32.What is the sum of the first 7 odd numbers (1 + 3 + 5 + …)? (a) 28 (b) 49 (c) 56 (d) 13
  33. 33.Which term of the AP 2, 10, 18, 26, … is 170? (a) 24th (b) 22nd (c) 21st (d) 23rd
  34. 34.What is the missing term in the AP 2, ?, 12, 17, 22? (a) 6 (b) 12 (c) 7 (d) 8
  35. 35.What is the 39th term of the AP 8, 10, 12, 14, …? (a) 78 (b) 86 (c) 76 (d) 84
  36. 36.What is the 39th term of the AP 4, 6, 8, 10, …? (a) 76 (b) 78 (c) 80 (d) 82
  37. 37.What is the sum of the first 19 odd numbers (1 + 3 + 5 + …)? (a) 37 (b) 190 (c) 380 (d) 361
  38. 38.What is the sum of the first 15 odd numbers (1 + 3 + 5 + …)? (a) 240 (b) 225 (c) 29 (d) 120
  39. 39.What is the sum of the first 25 odd numbers (1 + 3 + 5 + …)? (a) 625 (b) 650 (c) 325 (d) 49
  40. 40.What is the 31st term of the AP 6, 11, 16, 21, …? (a) 161 (b) 150 (c) 155 (d) 156

Answer key

  1. 297
  2. 13
  3. 63
  4. 480
  5. 32nd
  6. 35th
  7. 95
  8. 4950
  9. 31
  10. 3655
  11. 170
  12. 11
  13. 59
  14. 29th
  15. 29th
  16. 222
  17. 529
  18. 54
  19. 45
  20. 19th
  21. 43
  22. 36th
  23. 3240
  24. 300
  25. 3081
  26. 1891
  27. 36
  28. 78
  29. 152
  30. 237
  31. 2016
  32. 49
  33. 22nd
  34. 7
  35. 84
  36. 80
  37. 361
  38. 225
  39. 625
  40. 156

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