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Arithmetic Progression Worksheet for Olympiad

Maths Olympiad topic 29: Sequences and AP · Set 776 · 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 50? (a) 1250 (b) 1225 (c) 2550 (d) 1275
  2. 2.Which term of the AP 18, 20, 22, 24, … is 82? (a) 33rd (b) 34th (c) 41st (d) 32nd
  3. 3.What is the sum of the first 11 terms of the AP 3, 7, 11, …? (a) 275 (b) 43 (c) 506 (d) 253
  4. 4.What is the sum of the first 6 terms of the AP 4, 9, 14, …? (a) 114 (b) 99 (c) 29 (d) 198
  5. 5.What is the 40th term of the AP 3, 6, 9, 12, …? (a) 117 (b) 121 (c) 123 (d) 120
  6. 6.What is the sum of the first 6 odd numbers (1 + 3 + 5 + …)? (a) 11 (b) 36 (c) 21 (d) 42
  7. 7.Which term of the AP 15, 19, 23, 27, … is 115? (a) 27th (b) 26th (c) 25th (d) 28th
  8. 8.What is the missing term in the AP 3, 10, 17, ?, 31? (a) 31 (b) 24 (c) 25 (d) 23
  9. 9.What is the sum of the first 7 terms of the AP 3, 8, 13, …? (a) 126 (b) 131 (c) 252 (d) 33
  10. 10.What is the missing term in the AP 2, 6, 10, ?, 18? (a) 14 (b) 15 (c) 13 (d) 18
  11. 11.What is the sum of the first 17 odd numbers (1 + 3 + 5 + …)? (a) 153 (b) 306 (c) 289 (d) 33
  12. 12.What is the sum of all the whole numbers from 1 to 89? (a) 3916 (b) 8010 (c) 4006 (d) 4005
  13. 13.What is the missing term in the AP 11, 17, 23, ?, 35? (a) 29 (b) 30 (c) 35 (d) 28
  14. 14.What is the 19th term of the AP 18, 24, 30, 36, …? (a) 114 (b) 108 (c) 132 (d) 126
  15. 15.What is the sum of the first 10 terms of the AP 8, 14, 20, …? (a) 62 (b) 700 (c) 350 (d) 380
  16. 16.What is the sum of the first 12 terms of the AP 1, 7, 13, …? (a) 67 (b) 816 (c) 444 (d) 408
  17. 17.What is the sum of all the whole numbers from 1 to 42? (a) 1806 (b) 882 (c) 903 (d) 861
  18. 18.What is the sum of all the whole numbers from 1 to 22? (a) 506 (b) 242 (c) 231 (d) 253
  19. 19.What is the sum of the first 11 terms of the AP 4, 9, 14, …? (a) 319 (b) 638 (c) 54 (d) 324
  20. 20.What is the missing term in the AP 19, 28, 37, ?, 55? (a) 45 (b) 46 (c) 55 (d) 47
  21. 21.What is the missing term in the AP 20, ?, 34, 41, 48? (a) 26 (b) 34 (c) 28 (d) 27
  22. 22.What is the 29th term of the AP 19, 26, 33, 40, …? (a) 215 (b) 222 (c) 196 (d) 203
  23. 23.What is the sum of the first 6 terms of the AP 2, 7, 12, …? (a) 87 (b) 174 (c) 102 (d) 27
  24. 24.What is the 14th term of the AP 17, 24, 31, 38, …? (a) 91 (b) 108 (c) 98 (d) 115
  25. 25.What is the missing term in the AP 4, 6, ?, 10, 12? (a) 9 (b) 8 (c) 7 (d) 10
  26. 26.What is the 19th term of the AP 17, 24, 31, 38, …? (a) 150 (b) 133 (c) 143 (d) 126
  27. 27.What is the sum of the first 8 terms of the AP 2, 4, 6, …? (a) 72 (b) 144 (c) 80 (d) 16
  28. 28.What is the sum of the first 5 odd numbers (1 + 3 + 5 + …)? (a) 30 (b) 15 (c) 9 (d) 25
  29. 29.What is the sum of the first 14 odd numbers (1 + 3 + 5 + …)? (a) 196 (b) 210 (c) 105 (d) 27
  30. 30.What is the 19th term of the AP 18, 21, 24, 27, …? (a) 57 (b) 72 (c) 75 (d) 54
  31. 31.What is the sum of the first 10 terms of the AP 1, 2, 3, …? (a) 10 (b) 55 (c) 110 (d) 60
  32. 32.What is the 38th term of the AP 3, 11, 19, 27, …? (a) 296 (b) 307 (c) 299 (d) 304
  33. 33.What is the 20th term of the AP 17, 22, 27, 32, …? (a) 112 (b) 117 (c) 95 (d) 100
  34. 34.What is the 17th term of the AP 16, 18, 20, 22, …? (a) 34 (b) 32 (c) 48 (d) 50
  35. 35.What is the sum of all the whole numbers from 1 to 11? (a) 132 (b) 67 (c) 66 (d) 55
  36. 36.What is the missing term in the AP 3, ?, 21, 30, 39? (a) 21 (b) 13 (c) 11 (d) 12
  37. 37.What is the sum of the first 12 terms of the AP 3, 7, 11, …? (a) 47 (b) 300 (c) 324 (d) 600
  38. 38.What is the sum of all the whole numbers from 1 to 52? (a) 1326 (b) 1378 (c) 1352 (d) 2756
  39. 39.What is the sum of all the whole numbers from 1 to 76? (a) 2888 (b) 2926 (c) 5852 (d) 2850
  40. 40.What is the missing term in the AP 2, 10, ?, 26, 34? (a) 26 (b) 18 (c) 17 (d) 19

Answer key

  1. 1275
  2. 33rd
  3. 253
  4. 99
  5. 120
  6. 36
  7. 26th
  8. 24
  9. 126
  10. 14
  11. 289
  12. 4005
  13. 29
  14. 126
  15. 350
  16. 408
  17. 903
  18. 253
  19. 319
  20. 46
  21. 27
  22. 215
  23. 87
  24. 108
  25. 8
  26. 143
  27. 72
  28. 25
  29. 196
  30. 72
  31. 55
  32. 299
  33. 112
  34. 48
  35. 66
  36. 12
  37. 300
  38. 1378
  39. 2926
  40. 18

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