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Arithmetic Progression Worksheet for Olympiad

Maths Olympiad topic 29: Sequences and AP · Set 584 · 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 7 terms of the AP 8, 10, 12, …? (a) 105 (b) 196 (c) 20 (d) 98
  2. 2.What is the sum of all the whole numbers from 1 to 61? (a) 1892 (b) 1830 (c) 3782 (d) 1891
  3. 3.What is the sum of all the whole numbers from 1 to 81? (a) 3321 (b) 6642 (c) 3240 (d) 3322
  4. 4.What is the missing term in the AP 15, 18, 21, ?, 27? (a) 25 (b) 27 (c) 24 (d) 23
  5. 5.What is the 37th term of the AP 8, 12, 16, 20, …? (a) 144 (b) 156 (c) 152 (d) 148
  6. 6.What is the 19th term of the AP 8, 14, 20, 26, …? (a) 114 (b) 108 (c) 122 (d) 116
  7. 7.What is the sum of the first 25 odd numbers (1 + 3 + 5 + …)? (a) 325 (b) 49 (c) 650 (d) 625
  8. 8.What is the missing term in the AP 3, ?, 19, 27, 35? (a) 12 (b) 10 (c) 19 (d) 11
  9. 9.What is the sum of all the whole numbers from 1 to 42? (a) 903 (b) 861 (c) 1806 (d) 882
  10. 10.What is the 25th term of the AP 3, 9, 15, 21, …? (a) 153 (b) 144 (c) 150 (d) 147
  11. 11.What is the 22nd term of the AP 6, 10, 14, 18, …? (a) 84 (b) 90 (c) 94 (d) 88
  12. 12.What is the 22nd term of the AP 18, 26, 34, 42, …? (a) 176 (b) 168 (c) 194 (d) 186
  13. 13.Which term of the AP 13, 15, 17, 19, … is 59? (a) 23rd (b) 25th (c) 24th (d) 26th
  14. 14.What is the sum of the first 7 terms of the AP 3, 6, 9, …? (a) 21 (b) 84 (c) 87 (d) 168
  15. 15.What is the sum of all the whole numbers from 1 to 49? (a) 1176 (b) 1226 (c) 2450 (d) 1225
  16. 16.What is the sum of the first 5 terms of the AP 3, 5, 7, …? (a) 11 (b) 70 (c) 35 (d) 40
  17. 17.What is the sum of all the whole numbers from 1 to 84? (a) 3570 (b) 3486 (c) 7140 (d) 3528
  18. 18.What is the sum of the first 9 terms of the AP 3, 4, 5, …? (a) 11 (b) 64 (c) 63 (d) 126
  19. 19.What is the sum of all the whole numbers from 1 to 19? (a) 380 (b) 190 (c) 171 (d) 191
  20. 20.What is the missing term in the AP 4, 12, 20, ?, 36? (a) 28 (b) 29 (c) 27 (d) 36
  21. 21.What is the sum of the first 12 terms of the AP 3, 6, 9, …? (a) 234 (b) 36 (c) 252 (d) 468
  22. 22.Which term of the AP 12, 15, 18, 21, … is 96? (a) 29th (b) 32nd (c) 30th (d) 28th
  23. 23.What is the missing term in the AP 7, 15, ?, 31, 39? (a) 24 (b) 31 (c) 23 (d) 22
  24. 24.What is the 20th term of the AP 12, 17, 22, 27, …? (a) 100 (b) 95 (c) 107 (d) 112
  25. 25.What is the sum of all the whole numbers from 1 to 21? (a) 232 (b) 462 (c) 210 (d) 231
  26. 26.What is the 18th term of the AP 6, 12, 18, 24, …? (a) 102 (b) 109 (c) 114 (d) 108
  27. 27.Which term of the AP 12, 14, 16, 18, … is 48? (a) 18th (b) 19th (c) 24th (d) 20th
  28. 28.What is the sum of the first 20 odd numbers (1 + 3 + 5 + …)? (a) 210 (b) 39 (c) 420 (d) 400
  29. 29.What is the 39th term of the AP 19, 24, 29, 34, …? (a) 209 (b) 190 (c) 195 (d) 214
  30. 30.What is the sum of the first 10 terms of the AP 9, 13, 17, …? (a) 290 (b) 45 (c) 270 (d) 540
  31. 31.What is the 20th term of the AP 19, 26, 33, 40, …? (a) 152 (b) 140 (c) 133 (d) 159
  32. 32.What is the missing term in the AP 3, ?, 17, 24, 31? (a) 17 (b) 10 (c) 11 (d) 9
  33. 33.What is the sum of the first 8 terms of the AP 7, 9, 11, …? (a) 120 (b) 21 (c) 112 (d) 224
  34. 34.What is the sum of the first 7 terms of the AP 2, 5, 8, …? (a) 80 (b) 77 (c) 154 (d) 20
  35. 35.Which term of the AP 16, 24, 32, 40, … is 280? (a) 35th (b) 34th (c) 33rd (d) 36th
  36. 36.What is the missing term in the AP 11, 17, ?, 29, 35? (a) 29 (b) 23 (c) 24 (d) 22
  37. 37.What is the 38th term of the AP 4, 6, 8, 10, …? (a) 80 (b) 76 (c) 78 (d) 74
  38. 38.What is the sum of the first 8 terms of the AP 3, 6, 9, …? (a) 216 (b) 120 (c) 24 (d) 108
  39. 39.What is the 24th term of the AP 13, 20, 27, 34, …? (a) 181 (b) 161 (c) 174 (d) 168
  40. 40.What is the 23rd term of the AP 7, 14, 21, 28, …? (a) 161 (b) 154 (c) 162 (d) 168

Answer key

  1. 98
  2. 1891
  3. 3321
  4. 24
  5. 152
  6. 116
  7. 625
  8. 11
  9. 903
  10. 147
  11. 90
  12. 186
  13. 24th
  14. 84
  15. 1225
  16. 35
  17. 3570
  18. 63
  19. 190
  20. 28
  21. 234
  22. 29th
  23. 23
  24. 107
  25. 231
  26. 108
  27. 19th
  28. 400
  29. 209
  30. 270
  31. 152
  32. 10
  33. 112
  34. 77
  35. 34th
  36. 23
  37. 78
  38. 108
  39. 174
  40. 161

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