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Arithmetic Progression Worksheet for Olympiad

Maths Olympiad topic 29: Sequences and AP · Set 310 · 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 5 odd numbers (1 + 3 + 5 + …)? (a) 30 (b) 9 (c) 15 (d) 25
  2. 2.What is the 26th term of the AP 12, 15, 18, 21, …? (a) 87 (b) 78 (c) 90 (d) 75
  3. 3.What is the sum of the first 8 terms of the AP 7, 8, 9, …? (a) 84 (b) 14 (c) 88 (d) 168
  4. 4.What is the sum of the first 7 terms of the AP 1, 2, 3, …? (a) 56 (b) 7 (c) 28 (d) 29
  5. 5.What is the 32nd term of the AP 20, 26, 32, 38, …? (a) 206 (b) 192 (c) 212 (d) 186
  6. 6.What is the missing term in the AP 10, 17, 24, ?, 38? (a) 32 (b) 31 (c) 38 (d) 30
  7. 7.Which term of the AP 1, 4, 7, 10, … is 46? (a) 17th (b) 16th (c) 15th (d) 18th
  8. 8.What is the 40th term of the AP 16, 20, 24, 28, …? (a) 172 (b) 156 (c) 160 (d) 176
  9. 9.What is the 38th term of the AP 10, 12, 14, 16, …? (a) 86 (b) 84 (c) 76 (d) 74
  10. 10.What is the 31st term of the AP 16, 19, 22, 25, …? (a) 106 (b) 93 (c) 90 (d) 109
  11. 11.What is the 33rd term of the AP 2, 6, 10, 14, …? (a) 134 (b) 132 (c) 128 (d) 130
  12. 12.What is the sum of the first 15 odd numbers (1 + 3 + 5 + …)? (a) 120 (b) 29 (c) 240 (d) 225
  13. 13.Which term of the AP 11, 13, 15, 17, … is 41? (a) 18th (b) 17th (c) 16th (d) 15th
  14. 14.Which term of the AP 20, 28, 36, 44, … is 276? (a) 33rd (b) 34th (c) 35th (d) 32nd
  15. 15.What is the missing term in the AP 2, ?, 16, 23, 30? (a) 8 (b) 10 (c) 16 (d) 9
  16. 16.What is the sum of all the whole numbers from 1 to 68? (a) 2312 (b) 2278 (c) 4692 (d) 2346
  17. 17.What is the sum of the first 5 terms of the AP 3, 4, 5, …? (a) 50 (b) 26 (c) 7 (d) 25
  18. 18.What is the sum of all the whole numbers from 1 to 10? (a) 45 (b) 110 (c) 55 (d) 50
  19. 19.What is the 24th term of the AP 16, 24, 32, 40, …? (a) 208 (b) 192 (c) 184 (d) 200
  20. 20.What is the 25th term of the AP 7, 10, 13, 16, …? (a) 82 (b) 72 (c) 75 (d) 79
  21. 21.What is the sum of all the whole numbers from 1 to 20? (a) 420 (b) 200 (c) 190 (d) 210
  22. 22.What is the missing term in the AP 14, 17, ?, 23, 26? (a) 23 (b) 19 (c) 21 (d) 20
  23. 23.What is the missing term in the AP 5, 14, 23, ?, 41? (a) 31 (b) 41 (c) 32 (d) 33
  24. 24.What is the 34th term of the AP 20, 27, 34, 41, …? (a) 258 (b) 251 (c) 238 (d) 231
  25. 25.What is the 38th term of the AP 7, 14, 21, 28, …? (a) 273 (b) 266 (c) 267 (d) 259
  26. 26.What is the 40th term of the AP 2, 10, 18, 26, …? (a) 320 (b) 322 (c) 314 (d) 312
  27. 27.What is the sum of the first 12 terms of the AP 3, 4, 5, …? (a) 204 (b) 14 (c) 102 (d) 108
  28. 28.What is the sum of all the whole numbers from 1 to 30? (a) 450 (b) 930 (c) 465 (d) 435
  29. 29.Which term of the AP 6, 8, 10, 12, … is 54? (a) 26th (b) 24th (c) 25th (d) 27th
  30. 30.What is the sum of all the whole numbers from 1 to 62? (a) 1922 (b) 1953 (c) 1891 (d) 3906
  31. 31.What is the sum of the first 8 terms of the AP 10, 13, 16, …? (a) 31 (b) 176 (c) 328 (d) 164
  32. 32.What is the 22nd term of the AP 8, 11, 14, 17, …? (a) 66 (b) 63 (c) 71 (d) 74
  33. 33.Which term of the AP 12, 18, 24, 30, … is 162? (a) 26th (b) 28th (c) 27th (d) 25th
  34. 34.What is the sum of the first 6 terms of the AP 3, 9, 15, …? (a) 33 (b) 216 (c) 126 (d) 108
  35. 35.What is the sum of the first 10 odd numbers (1 + 3 + 5 + …)? (a) 19 (b) 100 (c) 55 (d) 110
  36. 36.What is the sum of the first 24 odd numbers (1 + 3 + 5 + …)? (a) 300 (b) 47 (c) 576 (d) 600
  37. 37.What is the 35th term of the AP 4, 10, 16, 22, …? (a) 210 (b) 208 (c) 214 (d) 204
  38. 38.What is the sum of the first 9 terms of the AP 10, 15, 20, …? (a) 275 (b) 540 (c) 270 (d) 50
  39. 39.What is the missing term in the AP 11, 19, ?, 35, 43? (a) 35 (b) 26 (c) 27 (d) 28
  40. 40.What is the sum of the first 6 terms of the AP 9, 14, 19, …? (a) 129 (b) 34 (c) 144 (d) 258

Answer key

  1. 25
  2. 87
  3. 84
  4. 28
  5. 206
  6. 31
  7. 16th
  8. 172
  9. 84
  10. 106
  11. 130
  12. 225
  13. 16th
  14. 33rd
  15. 9
  16. 2346
  17. 25
  18. 55
  19. 200
  20. 79
  21. 210
  22. 20
  23. 32
  24. 251
  25. 266
  26. 314
  27. 102
  28. 465
  29. 25th
  30. 1953
  31. 164
  32. 71
  33. 26th
  34. 108
  35. 100
  36. 576
  37. 208
  38. 270
  39. 27
  40. 129

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