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Arithmetic Progression Worksheet for Olympiad

Maths Olympiad topic 29: Sequences and AP · Set 364 · 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 29th term of the AP 2, 4, 6, 8, …? (a) 60 (b) 59 (c) 56 (d) 58
  2. 2.Which term of the AP 5, 12, 19, 26, … is 243? (a) 36th (b) 34th (c) 37th (d) 35th
  3. 3.What is the 36th term of the AP 19, 26, 33, 40, …? (a) 271 (b) 252 (c) 264 (d) 245
  4. 4.Which term of the AP 4, 7, 10, 13, … is 55? (a) 19th (b) 20th (c) 18th (d) 17th
  5. 5.What is the 38th term of the AP 14, 18, 22, 26, …? (a) 162 (b) 148 (c) 166 (d) 152
  6. 6.What is the sum of the first 6 terms of the AP 5, 10, 15, …? (a) 30 (b) 105 (c) 120 (d) 210
  7. 7.Which term of the AP 1, 3, 5, 7, … is 23? (a) 14th (b) 12th (c) 13th (d) 11th
  8. 8.What is the sum of the first 5 terms of the AP 8, 10, 12, …? (a) 65 (b) 16 (c) 60 (d) 120
  9. 9.What is the sum of all the whole numbers from 1 to 21? (a) 462 (b) 231 (c) 210 (d) 232
  10. 10.What is the 34th term of the AP 19, 21, 23, 25, …? (a) 66 (b) 85 (c) 68 (d) 87
  11. 11.What is the sum of all the whole numbers from 1 to 27? (a) 378 (b) 379 (c) 756 (d) 351
  12. 12.Which term of the AP 8, 11, 14, 17, … is 29? (a) 7th (b) 8th (c) 10th (d) 9th
  13. 13.What is the sum of the first 6 terms of the AP 10, 14, 18, …? (a) 132 (b) 240 (c) 30 (d) 120
  14. 14.What is the missing term in the AP 3, ?, 17, 24, 31? (a) 10 (b) 17 (c) 11 (d) 9
  15. 15.What is the sum of the first 11 terms of the AP 4, 6, 8, …? (a) 24 (b) 154 (c) 308 (d) 165
  16. 16.What is the missing term in the AP 12, 15, 18, ?, 24? (a) 21 (b) 24 (c) 20 (d) 22
  17. 17.What is the missing term in the AP 10, 15, ?, 25, 30? (a) 25 (b) 19 (c) 21 (d) 20
  18. 18.What is the sum of the first 6 terms of the AP 9, 10, 11, …? (a) 138 (b) 14 (c) 69 (d) 72
  19. 19.What is the sum of the first 9 terms of the AP 10, 15, 20, …? (a) 50 (b) 275 (c) 540 (d) 270
  20. 20.What is the sum of all the whole numbers from 1 to 96? (a) 4560 (b) 4608 (c) 9312 (d) 4656
  21. 21.What is the missing term in the AP 4, 13, ?, 31, 40? (a) 21 (b) 22 (c) 23 (d) 31
  22. 22.What is the 12th term of the AP 1, 3, 5, 7, …? (a) 22 (b) 24 (c) 25 (d) 23
  23. 23.What is the sum of the first 25 odd numbers (1 + 3 + 5 + …)? (a) 325 (b) 625 (c) 650 (d) 49
  24. 24.What is the sum of all the whole numbers from 1 to 91? (a) 8372 (b) 4187 (c) 4095 (d) 4186
  25. 25.What is the sum of the first 5 terms of the AP 2, 5, 8, …? (a) 14 (b) 40 (c) 80 (d) 43
  26. 26.Which term of the AP 12, 14, 16, 18, … is 90? (a) 41st (b) 45th (c) 39th (d) 40th
  27. 27.What is the sum of the first 8 terms of the AP 10, 15, 20, …? (a) 45 (b) 220 (c) 440 (d) 240
  28. 28.What is the 13th term of the AP 10, 13, 16, 19, …? (a) 49 (b) 39 (c) 36 (d) 46
  29. 29.What is the 38th term of the AP 15, 17, 19, 21, …? (a) 89 (b) 76 (c) 74 (d) 91
  30. 30.What is the 18th term of the AP 2, 7, 12, 17, …? (a) 90 (b) 92 (c) 87 (d) 85
  31. 31.What is the sum of the first 5 terms of the AP 3, 8, 13, …? (a) 70 (b) 130 (c) 23 (d) 65
  32. 32.What is the 37th term of the AP 4, 9, 14, 19, …? (a) 189 (b) 180 (c) 185 (d) 184
  33. 33.What is the sum of all the whole numbers from 1 to 90? (a) 4050 (b) 8190 (c) 4005 (d) 4095
  34. 34.What is the sum of all the whole numbers from 1 to 16? (a) 128 (b) 120 (c) 272 (d) 136
  35. 35.What is the missing term in the AP 6, 10, ?, 18, 22? (a) 18 (b) 15 (c) 13 (d) 14
  36. 36.What is the 12th term of the AP 3, 6, 9, 12, …? (a) 37 (b) 36 (c) 33 (d) 39
  37. 37.Which term of the AP 17, 22, 27, 32, … is 147? (a) 29th (b) 26th (c) 27th (d) 28th
  38. 38.What is the missing term in the AP 5, 7, 9, ?, 13? (a) 11 (b) 10 (c) 12 (d) 13
  39. 39.What is the missing term in the AP 18, 24, 30, ?, 42? (a) 35 (b) 42 (c) 36 (d) 37
  40. 40.Which term of the AP 4, 8, 12, 16, … is 60? (a) 14th (b) 16th (c) 17th (d) 15th

Answer key

  1. 58
  2. 35th
  3. 264
  4. 18th
  5. 162
  6. 105
  7. 12th
  8. 60
  9. 231
  10. 85
  11. 378
  12. 8th
  13. 120
  14. 10
  15. 154
  16. 21
  17. 20
  18. 69
  19. 270
  20. 4656
  21. 22
  22. 23
  23. 625
  24. 4186
  25. 40
  26. 40th
  27. 220
  28. 46
  29. 89
  30. 87
  31. 65
  32. 184
  33. 4095
  34. 136
  35. 14
  36. 36
  37. 27th
  38. 11
  39. 36
  40. 15th

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