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Arithmetic Progression Worksheet for Olympiad

Maths Olympiad topic 29: Sequences and AP · Set 99 · 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 33? (a) 1122 (b) 561 (c) 562 (d) 528
  2. 2.What is the sum of the first 6 odd numbers (1 + 3 + 5 + …)? (a) 42 (b) 21 (c) 36 (d) 11
  3. 3.What is the sum of the first 13 odd numbers (1 + 3 + 5 + …)? (a) 182 (b) 169 (c) 91 (d) 25
  4. 4.What is the sum of the first 19 odd numbers (1 + 3 + 5 + …)? (a) 380 (b) 361 (c) 37 (d) 190
  5. 5.What is the 37th term of the AP 19, 22, 25, 28, …? (a) 108 (b) 130 (c) 127 (d) 111
  6. 6.What is the 17th term of the AP 11, 20, 29, 38, …? (a) 153 (b) 155 (c) 144 (d) 164
  7. 7.What is the sum of the first 6 terms of the AP 7, 10, 13, …? (a) 96 (b) 22 (c) 87 (d) 174
  8. 8.What is the sum of the first 10 odd numbers (1 + 3 + 5 + …)? (a) 110 (b) 55 (c) 100 (d) 19
  9. 9.What is the 31st term of the AP 20, 26, 32, 38, …? (a) 180 (b) 206 (c) 186 (d) 200
  10. 10.What is the sum of the first 28 odd numbers (1 + 3 + 5 + …)? (a) 812 (b) 55 (c) 406 (d) 784
  11. 11.Which term of the AP 1, 5, 9, 13, … is 133? (a) 35th (b) 34th (c) 33rd (d) 36th
  12. 12.What is the 32nd term of the AP 17, 21, 25, 29, …? (a) 145 (b) 141 (c) 128 (d) 124
  13. 13.What is the sum of the first 6 terms of the AP 8, 12, 16, …? (a) 120 (b) 28 (c) 216 (d) 108
  14. 14.What is the 17th term of the AP 17, 20, 23, 26, …? (a) 68 (b) 48 (c) 51 (d) 65
  15. 15.What is the 23rd term of the AP 11, 18, 25, 32, …? (a) 161 (b) 154 (c) 165 (d) 172
  16. 16.What is the 28th term of the AP 10, 16, 22, 28, …? (a) 168 (b) 172 (c) 162 (d) 178
  17. 17.Which term of the AP 17, 23, 29, 35, … is 161? (a) 24th (b) 26th (c) 27th (d) 25th
  18. 18.What is the missing term in the AP 13, 20, 27, ?, 41? (a) 34 (b) 35 (c) 41 (d) 33
  19. 19.What is the 37th term of the AP 3, 6, 9, 12, …? (a) 112 (b) 108 (c) 114 (d) 111
  20. 20.What is the sum of the first 5 terms of the AP 2, 4, 6, …? (a) 60 (b) 10 (c) 30 (d) 35
  21. 21.Which term of the AP 16, 25, 34, 43, … is 133? (a) 13th (b) 15th (c) 14th (d) 16th
  22. 22.What is the 33rd term of the AP 17, 22, 27, 32, …? (a) 182 (b) 160 (c) 165 (d) 177
  23. 23.What is the 28th term of the AP 6, 9, 12, 15, …? (a) 81 (b) 84 (c) 90 (d) 87
  24. 24.What is the sum of the first 12 terms of the AP 6, 9, 12, …? (a) 540 (b) 39 (c) 270 (d) 288
  25. 25.What is the sum of the first 12 terms of the AP 3, 7, 11, …? (a) 600 (b) 324 (c) 300 (d) 47
  26. 26.What is the 29th term of the AP 8, 16, 24, 32, …? (a) 224 (b) 232 (c) 240 (d) 233
  27. 27.What is the 29th term of the AP 11, 18, 25, 32, …? (a) 203 (b) 214 (c) 196 (d) 207
  28. 28.What is the sum of the first 6 terms of the AP 4, 7, 10, …? (a) 138 (b) 78 (c) 19 (d) 69
  29. 29.Which term of the AP 14, 18, 22, 26, … is 98? (a) 24th (b) 21st (c) 23rd (d) 22nd
  30. 30.What is the 21st term of the AP 8, 12, 16, 20, …? (a) 88 (b) 80 (c) 92 (d) 84
  31. 31.What is the missing term in the AP 6, ?, 10, 12, 14? (a) 7 (b) 9 (c) 8 (d) 10
  32. 32.What is the sum of all the whole numbers from 1 to 47? (a) 2256 (b) 1081 (c) 1128 (d) 1129
  33. 33.What is the sum of the first 11 terms of the AP 4, 9, 14, …? (a) 319 (b) 638 (c) 324 (d) 54
  34. 34.What is the missing term in the AP 10, 15, ?, 25, 30? (a) 21 (b) 20 (c) 25 (d) 19
  35. 35.What is the sum of the first 14 odd numbers (1 + 3 + 5 + …)? (a) 196 (b) 27 (c) 210 (d) 105
  36. 36.What is the sum of the first 12 odd numbers (1 + 3 + 5 + …)? (a) 78 (b) 156 (c) 23 (d) 144
  37. 37.What is the sum of all the whole numbers from 1 to 80? (a) 3160 (b) 6480 (c) 3200 (d) 3240
  38. 38.What is the 25th term of the AP 6, 10, 14, 18, …? (a) 96 (b) 106 (c) 100 (d) 102
  39. 39.What is the sum of all the whole numbers from 1 to 15? (a) 240 (b) 120 (c) 121 (d) 105
  40. 40.What is the 33rd term of the AP 6, 9, 12, 15, …? (a) 96 (b) 102 (c) 105 (d) 99

Answer key

  1. 561
  2. 36
  3. 169
  4. 361
  5. 127
  6. 155
  7. 87
  8. 100
  9. 200
  10. 784
  11. 34th
  12. 141
  13. 108
  14. 65
  15. 165
  16. 172
  17. 25th
  18. 34
  19. 111
  20. 30
  21. 14th
  22. 177
  23. 87
  24. 270
  25. 300
  26. 232
  27. 207
  28. 69
  29. 22nd
  30. 88
  31. 8
  32. 1128
  33. 319
  34. 20
  35. 196
  36. 144
  37. 3240
  38. 102
  39. 120
  40. 102

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