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Arithmetic Progression Worksheet for Olympiad

Maths Olympiad topic 29: Sequences and AP · Set 943 · 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 10 odd numbers (1 + 3 + 5 + …)? (a) 110 (b) 55 (c) 100 (d) 19
  2. 2.What is the 27th term of the AP 12, 18, 24, 30, …? (a) 168 (b) 156 (c) 174 (d) 162
  3. 3.What is the sum of the first 10 terms of the AP 9, 11, 13, …? (a) 360 (b) 27 (c) 180 (d) 190
  4. 4.Which term of the AP 20, 26, 32, 38, … is 164? (a) 27th (b) 24th (c) 25th (d) 26th
  5. 5.What is the sum of all the whole numbers from 1 to 81? (a) 3240 (b) 3321 (c) 6642 (d) 3322
  6. 6.Which term of the AP 6, 12, 18, 24, … is 228? (a) 38th (b) 39th (c) 40th (d) 37th
  7. 7.What is the 29th term of the AP 2, 8, 14, 20, …? (a) 174 (b) 176 (c) 168 (d) 170
  8. 8.Which term of the AP 6, 13, 20, 27, … is 188? (a) 29th (b) 28th (c) 26th (d) 27th
  9. 9.What is the 20th term of the AP 12, 20, 28, 36, …? (a) 152 (b) 164 (c) 172 (d) 160
  10. 10.Which term of the AP 15, 24, 33, 42, … is 231? (a) 27th (b) 25th (c) 24th (d) 26th
  11. 11.What is the sum of the first 19 odd numbers (1 + 3 + 5 + …)? (a) 190 (b) 361 (c) 37 (d) 380
  12. 12.What is the missing term in the AP 2, ?, 6, 8, 10? (a) 4 (b) 6 (c) 3 (d) 5
  13. 13.What is the missing term in the AP 9, ?, 17, 21, 25? (a) 12 (b) 13 (c) 14 (d) 17
  14. 14.Which term of the AP 18, 24, 30, 36, … is 216? (a) 35th (b) 34th (c) 36th (d) 33rd
  15. 15.What is the missing term in the AP 12, ?, 22, 27, 32? (a) 17 (b) 22 (c) 18 (d) 16
  16. 16.What is the 23rd term of the AP 9, 18, 27, 36, …? (a) 207 (b) 198 (c) 216 (d) 208
  17. 17.What is the sum of the first 26 odd numbers (1 + 3 + 5 + …)? (a) 51 (b) 702 (c) 351 (d) 676
  18. 18.What is the sum of the first 9 terms of the AP 8, 11, 14, …? (a) 32 (b) 183 (c) 360 (d) 180
  19. 19.What is the 30th term of the AP 6, 11, 16, 21, …? (a) 145 (b) 150 (c) 151 (d) 156
  20. 20.What is the 33rd term of the AP 7, 13, 19, 25, …? (a) 205 (b) 192 (c) 198 (d) 199
  21. 21.What is the sum of the first 29 odd numbers (1 + 3 + 5 + …)? (a) 57 (b) 841 (c) 870 (d) 435
  22. 22.What is the sum of all the whole numbers from 1 to 62? (a) 1953 (b) 1922 (c) 1891 (d) 3906
  23. 23.What is the sum of the first 8 terms of the AP 5, 8, 11, …? (a) 248 (b) 26 (c) 136 (d) 124
  24. 24.What is the sum of all the whole numbers from 1 to 20? (a) 190 (b) 420 (c) 210 (d) 200
  25. 25.What is the sum of the first 7 terms of the AP 2, 3, 4, …? (a) 35 (b) 36 (c) 8 (d) 70
  26. 26.What is the 36th term of the AP 8, 11, 14, 17, …? (a) 108 (b) 116 (c) 105 (d) 113
  27. 27.What is the 28th term of the AP 2, 5, 8, 11, …? (a) 81 (b) 84 (c) 86 (d) 83
  28. 28.What is the sum of all the whole numbers from 1 to 52? (a) 1352 (b) 1326 (c) 2756 (d) 1378
  29. 29.What is the sum of the first 9 terms of the AP 1, 7, 13, …? (a) 49 (b) 252 (c) 450 (d) 225
  30. 30.What is the sum of the first 8 terms of the AP 4, 6, 8, …? (a) 88 (b) 176 (c) 96 (d) 18
  31. 31.Which term of the AP 13, 16, 19, 22, … is 46? (a) 11th (b) 14th (c) 13th (d) 12th
  32. 32.What is the 40th term of the AP 18, 25, 32, 39, …? (a) 291 (b) 280 (c) 298 (d) 273
  33. 33.What is the sum of all the whole numbers from 1 to 80? (a) 6480 (b) 3200 (c) 3240 (d) 3160
  34. 34.What is the 13th term of the AP 2, 10, 18, 26, …? (a) 106 (b) 104 (c) 96 (d) 98
  35. 35.What is the 28th term of the AP 12, 15, 18, 21, …? (a) 81 (b) 84 (c) 93 (d) 96
  36. 36.What is the 16th term of the AP 7, 15, 23, 31, …? (a) 135 (b) 128 (c) 127 (d) 120
  37. 37.What is the 34th term of the AP 18, 23, 28, 33, …? (a) 170 (b) 165 (c) 188 (d) 183
  38. 38.What is the sum of all the whole numbers from 1 to 24? (a) 288 (b) 600 (c) 300 (d) 276
  39. 39.What is the 24th term of the AP 15, 18, 21, 24, …? (a) 84 (b) 87 (c) 72 (d) 69
  40. 40.Which term of the AP 17, 20, 23, 26, … is 59? (a) 17th (b) 15th (c) 14th (d) 16th

Answer key

  1. 100
  2. 168
  3. 180
  4. 25th
  5. 3321
  6. 38th
  7. 170
  8. 27th
  9. 164
  10. 25th
  11. 361
  12. 4
  13. 13
  14. 34th
  15. 17
  16. 207
  17. 676
  18. 180
  19. 151
  20. 199
  21. 841
  22. 1953
  23. 124
  24. 210
  25. 35
  26. 113
  27. 83
  28. 1378
  29. 225
  30. 88
  31. 12th
  32. 291
  33. 3240
  34. 98
  35. 93
  36. 127
  37. 183
  38. 300
  39. 84
  40. 15th

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