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Arithmetic Progression Worksheet for Olympiad

Maths Olympiad topic 29: Sequences and AP · Set 46 · 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 missing term in the AP 19, 25, 31, ?, 43? (a) 43 (b) 36 (c) 38 (d) 37
  2. 2.What is the sum of the first 10 terms of the AP 2, 7, 12, …? (a) 245 (b) 490 (c) 47 (d) 270
  3. 3.What is the 12th term of the AP 18, 20, 22, 24, …? (a) 42 (b) 22 (c) 40 (d) 24
  4. 4.What is the missing term in the AP 4, ?, 10, 13, 16? (a) 6 (b) 8 (c) 7 (d) 10
  5. 5.What is the sum of all the whole numbers from 1 to 20? (a) 200 (b) 420 (c) 190 (d) 210
  6. 6.What is the 34th term of the AP 12, 20, 28, 36, …? (a) 264 (b) 284 (c) 276 (d) 272
  7. 7.What is the 21st term of the AP 17, 23, 29, 35, …? (a) 143 (b) 120 (c) 126 (d) 137
  8. 8.What is the missing term in the AP 17, 21, ?, 29, 33? (a) 29 (b) 25 (c) 24 (d) 26
  9. 9.What is the 40th term of the AP 8, 10, 12, 14, …? (a) 78 (b) 80 (c) 86 (d) 88
  10. 10.What is the 38th term of the AP 11, 13, 15, 17, …? (a) 87 (b) 85 (c) 76 (d) 74
  11. 11.What is the missing term in the AP 7, ?, 11, 13, 15? (a) 8 (b) 10 (c) 11 (d) 9
  12. 12.What is the sum of the first 7 odd numbers (1 + 3 + 5 + …)? (a) 13 (b) 56 (c) 49 (d) 28
  13. 13.What is the sum of the first 30 odd numbers (1 + 3 + 5 + …)? (a) 900 (b) 59 (c) 465 (d) 930
  14. 14.What is the 10th term of the AP 6, 9, 12, 15, …? (a) 36 (b) 30 (c) 33 (d) 27
  15. 15.What is the 26th term of the AP 3, 11, 19, 27, …? (a) 211 (b) 200 (c) 203 (d) 208
  16. 16.What is the 16th term of the AP 2, 8, 14, 20, …? (a) 96 (b) 98 (c) 92 (d) 90
  17. 17.What is the sum of the first 12 terms of the AP 2, 5, 8, …? (a) 240 (b) 35 (c) 222 (d) 444
  18. 18.What is the 30th term of the AP 8, 10, 12, 14, …? (a) 66 (b) 60 (c) 58 (d) 68
  19. 19.What is the 25th term of the AP 4, 11, 18, 25, …? (a) 179 (b) 175 (c) 172 (d) 168
  20. 20.What is the 19th term of the AP 5, 10, 15, 20, …? (a) 96 (b) 90 (c) 95 (d) 100
  21. 21.What is the missing term in the AP 16, ?, 24, 28, 32? (a) 21 (b) 24 (c) 20 (d) 19
  22. 22.What is the sum of the first 8 terms of the AP 4, 5, 6, …? (a) 11 (b) 120 (c) 64 (d) 60
  23. 23.Which term of the AP 4, 7, 10, 13, … is 58? (a) 19th (b) 20th (c) 18th (d) 21st
  24. 24.What is the sum of the first 23 odd numbers (1 + 3 + 5 + …)? (a) 552 (b) 276 (c) 45 (d) 529
  25. 25.What is the sum of the first 8 terms of the AP 7, 9, 11, …? (a) 21 (b) 112 (c) 120 (d) 224
  26. 26.Which term of the AP 4, 9, 14, 19, … is 69? (a) 15th (b) 13th (c) 16th (d) 14th
  27. 27.Which term of the AP 17, 21, 25, 29, … is 173? (a) 42nd (b) 41st (c) 40th (d) 39th
  28. 28.What is the 31st term of the AP 1, 7, 13, 19, …? (a) 186 (b) 181 (c) 187 (d) 180
  29. 29.What is the sum of all the whole numbers from 1 to 48? (a) 1128 (b) 1176 (c) 2352 (d) 1152
  30. 30.What is the sum of the first 20 odd numbers (1 + 3 + 5 + …)? (a) 210 (b) 420 (c) 400 (d) 39
  31. 31.What is the 40th term of the AP 14, 18, 22, 26, …? (a) 160 (b) 174 (c) 156 (d) 170
  32. 32.What is the missing term in the AP 13, 19, 25, ?, 37? (a) 31 (b) 30 (c) 32 (d) 37
  33. 33.What is the 37th term of the AP 8, 17, 26, 35, …? (a) 324 (b) 333 (c) 341 (d) 332
  34. 34.What is the sum of the first 5 terms of the AP 7, 9, 11, …? (a) 110 (b) 60 (c) 55 (d) 15
  35. 35.What is the 25th term of the AP 7, 15, 23, 31, …? (a) 199 (b) 200 (c) 192 (d) 207
  36. 36.What is the 28th term of the AP 4, 6, 8, 10, …? (a) 60 (b) 56 (c) 58 (d) 54
  37. 37.What is the 27th term of the AP 18, 22, 26, 30, …? (a) 104 (b) 122 (c) 108 (d) 126
  38. 38.What is the sum of the first 5 terms of the AP 5, 8, 11, …? (a) 110 (b) 58 (c) 55 (d) 17
  39. 39.What is the sum of the first 17 odd numbers (1 + 3 + 5 + …)? (a) 306 (b) 289 (c) 153 (d) 33
  40. 40.What is the sum of the first 12 terms of the AP 2, 6, 10, …? (a) 46 (b) 576 (c) 288 (d) 312

Answer key

  1. 37
  2. 245
  3. 40
  4. 7
  5. 210
  6. 276
  7. 137
  8. 25
  9. 86
  10. 85
  11. 9
  12. 49
  13. 900
  14. 33
  15. 203
  16. 92
  17. 222
  18. 66
  19. 172
  20. 95
  21. 20
  22. 60
  23. 19th
  24. 529
  25. 112
  26. 14th
  27. 40th
  28. 181
  29. 1176
  30. 400
  31. 170
  32. 31
  33. 332
  34. 55
  35. 199
  36. 58
  37. 122
  38. 55
  39. 289
  40. 288

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