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Arithmetic Progression Worksheet for Olympiad

Maths Olympiad topic 29: Sequences and AP · Set 206 · 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.Which term of the AP 5, 8, 11, 14, … is 29? (a) 10th (b) 9th (c) 11th (d) 8th
  2. 2.What is the 29th term of the AP 17, 21, 25, 29, …? (a) 112 (b) 116 (c) 129 (d) 133
  3. 3.What is the 19th term of the AP 4, 11, 18, 25, …? (a) 133 (b) 130 (c) 126 (d) 137
  4. 4.Which term of the AP 10, 14, 18, 22, … is 150? (a) 36th (b) 38th (c) 37th (d) 35th
  5. 5.What is the sum of the first 11 terms of the AP 6, 11, 16, …? (a) 346 (b) 682 (c) 341 (d) 56
  6. 6.What is the sum of the first 5 terms of the AP 2, 3, 4, …? (a) 21 (b) 6 (c) 40 (d) 20
  7. 7.What is the sum of the first 6 terms of the AP 4, 8, 12, …? (a) 96 (b) 24 (c) 84 (d) 168
  8. 8.What is the sum of all the whole numbers from 1 to 54? (a) 1431 (b) 1485 (c) 2970 (d) 1458
  9. 9.What is the missing term in the AP 18, 25, 32, ?, 46? (a) 38 (b) 39 (c) 40 (d) 46
  10. 10.What is the sum of the first 5 terms of the AP 3, 5, 7, …? (a) 11 (b) 70 (c) 40 (d) 35
  11. 11.Which term of the AP 13, 22, 31, 40, … is 238? (a) 25th (b) 27th (c) 28th (d) 26th
  12. 12.What is the missing term in the AP 2, ?, 8, 11, 14? (a) 8 (b) 4 (c) 5 (d) 6
  13. 13.What is the sum of the first 17 odd numbers (1 + 3 + 5 + …)? (a) 153 (b) 306 (c) 289 (d) 33
  14. 14.What is the 13th term of the AP 4, 12, 20, 28, …? (a) 96 (b) 100 (c) 104 (d) 108
  15. 15.What is the 12th term of the AP 11, 16, 21, 26, …? (a) 55 (b) 66 (c) 60 (d) 71
  16. 16.What is the sum of the first 7 terms of the AP 5, 9, 13, …? (a) 238 (b) 119 (c) 133 (d) 29
  17. 17.Which term of the AP 1, 8, 15, 22, … is 141? (a) 21st (b) 23rd (c) 22nd (d) 20th
  18. 18.What is the sum of the first 9 terms of the AP 6, 9, 12, …? (a) 165 (b) 162 (c) 324 (d) 30
  19. 19.What is the sum of the first 6 terms of the AP 2, 7, 12, …? (a) 174 (b) 27 (c) 87 (d) 102
  20. 20.What is the sum of the first 7 terms of the AP 2, 8, 14, …? (a) 161 (b) 38 (c) 140 (d) 280
  21. 21.What is the sum of all the whole numbers from 1 to 95? (a) 9120 (b) 4561 (c) 4560 (d) 4465
  22. 22.What is the 16th term of the AP 5, 7, 9, 11, …? (a) 32 (b) 35 (c) 37 (d) 30
  23. 23.What is the 22nd term of the AP 4, 10, 16, 22, …? (a) 126 (b) 132 (c) 130 (d) 136
  24. 24.What is the sum of the first 26 odd numbers (1 + 3 + 5 + …)? (a) 676 (b) 351 (c) 702 (d) 51
  25. 25.What is the 11th term of the AP 11, 13, 15, 17, …? (a) 22 (b) 33 (c) 20 (d) 31
  26. 26.What is the missing term in the AP 20, ?, 34, 41, 48? (a) 34 (b) 27 (c) 28 (d) 26
  27. 27.Which term of the AP 4, 13, 22, 31, … is 310? (a) 35th (b) 34th (c) 37th (d) 36th
  28. 28.What is the sum of all the whole numbers from 1 to 19? (a) 191 (b) 171 (c) 380 (d) 190
  29. 29.What is the sum of all the whole numbers from 1 to 20? (a) 200 (b) 190 (c) 210 (d) 420
  30. 30.What is the 30th term of the AP 16, 21, 26, 31, …? (a) 161 (b) 166 (c) 145 (d) 150
  31. 31.What is the sum of all the whole numbers from 1 to 49? (a) 1225 (b) 2450 (c) 1226 (d) 1176
  32. 32.What is the 38th term of the AP 17, 25, 33, 41, …? (a) 313 (b) 296 (c) 321 (d) 304
  33. 33.What is the sum of the first 11 terms of the AP 5, 6, 7, …? (a) 110 (b) 220 (c) 15 (d) 111
  34. 34.What is the sum of the first 5 odd numbers (1 + 3 + 5 + …)? (a) 9 (b) 25 (c) 30 (d) 15
  35. 35.What is the 28th term of the AP 4, 11, 18, 25, …? (a) 189 (b) 193 (c) 196 (d) 200
  36. 36.What is the 16th term of the AP 3, 10, 17, 24, …? (a) 105 (b) 112 (c) 115 (d) 108
  37. 37.What is the sum of the first 7 terms of the AP 10, 12, 14, …? (a) 224 (b) 119 (c) 22 (d) 112
  38. 38.What is the 40th term of the AP 1, 5, 9, 13, …? (a) 161 (b) 156 (c) 160 (d) 157
  39. 39.What is the 12th term of the AP 1, 9, 17, 25, …? (a) 96 (b) 88 (c) 89 (d) 97
  40. 40.What is the sum of the first 10 odd numbers (1 + 3 + 5 + …)? (a) 55 (b) 110 (c) 100 (d) 19

Answer key

  1. 9th
  2. 129
  3. 130
  4. 36th
  5. 341
  6. 20
  7. 84
  8. 1485
  9. 39
  10. 35
  11. 26th
  12. 5
  13. 289
  14. 100
  15. 66
  16. 119
  17. 21st
  18. 162
  19. 87
  20. 140
  21. 4560
  22. 35
  23. 130
  24. 676
  25. 31
  26. 27
  27. 35th
  28. 190
  29. 210
  30. 161
  31. 1225
  32. 313
  33. 110
  34. 25
  35. 193
  36. 108
  37. 112
  38. 157
  39. 89
  40. 100

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