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Arithmetic Progression Worksheet for Olympiad

Maths Olympiad topic 29: Sequences and AP · Set 660 · 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 10? (a) 50 (b) 45 (c) 110 (d) 55
  2. 2.What is the sum of all the whole numbers from 1 to 42? (a) 882 (b) 861 (c) 1806 (d) 903
  3. 3.What is the sum of all the whole numbers from 1 to 25? (a) 325 (b) 326 (c) 650 (d) 300
  4. 4.What is the sum of the first 30 odd numbers (1 + 3 + 5 + …)? (a) 465 (b) 59 (c) 900 (d) 930
  5. 5.What is the sum of the first 5 odd numbers (1 + 3 + 5 + …)? (a) 25 (b) 15 (c) 30 (d) 9
  6. 6.Which term of the AP 16, 25, 34, 43, … is 322? (a) 34th (b) 36th (c) 35th (d) 37th
  7. 7.What is the sum of all the whole numbers from 1 to 50? (a) 1275 (b) 1225 (c) 1250 (d) 2550
  8. 8.What is the 18th term of the AP 4, 7, 10, 13, …? (a) 51 (b) 55 (c) 54 (d) 58
  9. 9.What is the 23rd term of the AP 15, 18, 21, 24, …? (a) 66 (b) 81 (c) 69 (d) 84
  10. 10.What is the 34th term of the AP 12, 20, 28, 36, …? (a) 264 (b) 276 (c) 284 (d) 272
  11. 11.What is the sum of all the whole numbers from 1 to 20? (a) 420 (b) 200 (c) 190 (d) 210
  12. 12.What is the sum of the first 6 terms of the AP 10, 13, 16, …? (a) 210 (b) 105 (c) 114 (d) 25
  13. 13.What is the sum of the first 8 terms of the AP 9, 14, 19, …? (a) 44 (b) 424 (c) 212 (d) 232
  14. 14.What is the 26th term of the AP 14, 17, 20, 23, …? (a) 75 (b) 78 (c) 92 (d) 89
  15. 15.Which term of the AP 11, 13, 15, 17, … is 73? (a) 34th (b) 31st (c) 33rd (d) 32nd
  16. 16.What is the 18th term of the AP 1, 3, 5, 7, …? (a) 36 (b) 34 (c) 35 (d) 37
  17. 17.What is the missing term in the AP 15, 21, 27, ?, 39? (a) 32 (b) 33 (c) 39 (d) 34
  18. 18.Which term of the AP 5, 9, 13, 17, … is 89? (a) 24th (b) 22nd (c) 21st (d) 23rd
  19. 19.Which term of the AP 2, 9, 16, 23, … is 170? (a) 27th (b) 25th (c) 24th (d) 26th
  20. 20.What is the sum of all the whole numbers from 1 to 19? (a) 191 (b) 380 (c) 171 (d) 190
  21. 21.What is the sum of all the whole numbers from 1 to 77? (a) 6006 (b) 3003 (c) 3004 (d) 2926
  22. 22.What is the 38th term of the AP 20, 28, 36, 44, …? (a) 296 (b) 324 (c) 316 (d) 304
  23. 23.What is the sum of all the whole numbers from 1 to 61? (a) 1892 (b) 3782 (c) 1891 (d) 1830
  24. 24.What is the 29th term of the AP 8, 14, 20, 26, …? (a) 182 (b) 168 (c) 176 (d) 174
  25. 25.What is the sum of all the whole numbers from 1 to 18? (a) 153 (b) 342 (c) 162 (d) 171
  26. 26.What is the sum of all the whole numbers from 1 to 83? (a) 6972 (b) 3403 (c) 3487 (d) 3486
  27. 27.Which term of the AP 10, 15, 20, 25, … is 55? (a) 10th (b) 12th (c) 11th (d) 9th
  28. 28.What is the sum of the first 6 terms of the AP 4, 9, 14, …? (a) 114 (b) 29 (c) 198 (d) 99
  29. 29.What is the 26th term of the AP 13, 16, 19, 22, …? (a) 78 (b) 75 (c) 88 (d) 91
  30. 30.What is the sum of the first 12 odd numbers (1 + 3 + 5 + …)? (a) 78 (b) 23 (c) 156 (d) 144
  31. 31.What is the 18th term of the AP 2, 5, 8, 11, …? (a) 56 (b) 53 (c) 54 (d) 51
  32. 32.What is the sum of the first 7 terms of the AP 1, 4, 7, …? (a) 140 (b) 19 (c) 73 (d) 70
  33. 33.What is the missing term in the AP 1, 5, ?, 13, 17? (a) 10 (b) 8 (c) 9 (d) 13
  34. 34.What is the sum of all the whole numbers from 1 to 11? (a) 55 (b) 67 (c) 66 (d) 132
  35. 35.What is the missing term in the AP 11, 19, 27, ?, 43? (a) 34 (b) 35 (c) 43 (d) 36
  36. 36.What is the sum of all the whole numbers from 1 to 45? (a) 1036 (b) 1035 (c) 990 (d) 2070
  37. 37.What is the 30th term of the AP 13, 16, 19, 22, …? (a) 100 (b) 87 (c) 103 (d) 90
  38. 38.What is the 36th term of the AP 17, 19, 21, 23, …? (a) 70 (b) 72 (c) 89 (d) 87
  39. 39.What is the sum of all the whole numbers from 1 to 80? (a) 3160 (b) 3200 (c) 6480 (d) 3240
  40. 40.What is the missing term in the AP 6, ?, 12, 15, 18? (a) 9 (b) 8 (c) 10 (d) 12

Answer key

  1. 55
  2. 903
  3. 325
  4. 900
  5. 25
  6. 35th
  7. 1275
  8. 55
  9. 81
  10. 276
  11. 210
  12. 105
  13. 212
  14. 89
  15. 32nd
  16. 35
  17. 33
  18. 22nd
  19. 25th
  20. 190
  21. 3003
  22. 316
  23. 1891
  24. 176
  25. 171
  26. 3486
  27. 10th
  28. 99
  29. 88
  30. 144
  31. 53
  32. 70
  33. 9
  34. 66
  35. 35
  36. 1035
  37. 100
  38. 87
  39. 3240
  40. 9

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