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Arithmetic Progression Worksheet for Olympiad

Maths Olympiad topic 29: Sequences and AP · Set 30 · 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 14, 18, ?, 26, 30? (a) 21 (b) 23 (c) 22 (d) 26
  2. 2.What is the sum of the first 12 terms of the AP 9, 11, 13, …? (a) 252 (b) 31 (c) 240 (d) 480
  3. 3.What is the 13th term of the AP 19, 22, 25, 28, …? (a) 36 (b) 39 (c) 58 (d) 55
  4. 4.What is the 30th term of the AP 2, 4, 6, 8, …? (a) 61 (b) 60 (c) 62 (d) 58
  5. 5.Which term of the AP 3, 7, 11, 15, … is 83? (a) 20th (b) 23rd (c) 21st (d) 22nd
  6. 6.What is the 24th term of the AP 17, 24, 31, 38, …? (a) 168 (b) 161 (c) 178 (d) 185
  7. 7.What is the missing term in the AP 11, 14, ?, 20, 23? (a) 18 (b) 17 (c) 20 (d) 16
  8. 8.What is the sum of the first 6 odd numbers (1 + 3 + 5 + …)? (a) 21 (b) 36 (c) 11 (d) 42
  9. 9.What is the 11th term of the AP 11, 15, 19, 23, …? (a) 40 (b) 51 (c) 44 (d) 55
  10. 10.Which term of the AP 6, 14, 22, 30, … is 158? (a) 19th (b) 20th (c) 22nd (d) 21st
  11. 11.What is the sum of all the whole numbers from 1 to 24? (a) 288 (b) 600 (c) 276 (d) 300
  12. 12.What is the sum of all the whole numbers from 1 to 71? (a) 5112 (b) 2557 (c) 2485 (d) 2556
  13. 13.What is the 20th term of the AP 9, 12, 15, 18, …? (a) 69 (b) 66 (c) 60 (d) 57
  14. 14.What is the 10th term of the AP 13, 18, 23, 28, …? (a) 45 (b) 50 (c) 63 (d) 58
  15. 15.What is the missing term in the AP 20, ?, 26, 29, 32? (a) 24 (b) 23 (c) 22 (d) 26
  16. 16.Which term of the AP 16, 25, 34, 43, … is 259? (a) 29th (b) 27th (c) 30th (d) 28th
  17. 17.What is the sum of the first 5 terms of the AP 1, 5, 9, …? (a) 55 (b) 45 (c) 17 (d) 90
  18. 18.What is the 26th term of the AP 19, 26, 33, 40, …? (a) 175 (b) 182 (c) 201 (d) 194
  19. 19.What is the 18th term of the AP 18, 26, 34, 42, …? (a) 162 (b) 154 (c) 136 (d) 144
  20. 20.What is the sum of the first 12 terms of the AP 7, 8, 9, …? (a) 300 (b) 18 (c) 150 (d) 156
  21. 21.What is the sum of the first 10 terms of the AP 2, 8, 14, …? (a) 320 (b) 580 (c) 56 (d) 290
  22. 22.What is the sum of all the whole numbers from 1 to 25? (a) 300 (b) 650 (c) 325 (d) 326
  23. 23.What is the missing term in the AP 8, 16, 24, ?, 40? (a) 31 (b) 40 (c) 33 (d) 32
  24. 24.What is the 22nd term of the AP 7, 15, 23, 31, …? (a) 168 (b) 183 (c) 176 (d) 175
  25. 25.What is the 24th term of the AP 5, 7, 9, 11, …? (a) 48 (b) 53 (c) 51 (d) 46
  26. 26.What is the sum of the first 16 odd numbers (1 + 3 + 5 + …)? (a) 272 (b) 256 (c) 31 (d) 136
  27. 27.What is the sum of the first 7 odd numbers (1 + 3 + 5 + …)? (a) 49 (b) 56 (c) 28 (d) 13
  28. 28.Which term of the AP 1, 7, 13, 19, … is 223? (a) 39th (b) 38th (c) 37th (d) 40th
  29. 29.What is the 16th term of the AP 5, 7, 9, 11, …? (a) 37 (b) 35 (c) 32 (d) 30
  30. 30.What is the sum of all the whole numbers from 1 to 40? (a) 820 (b) 800 (c) 1640 (d) 780
  31. 31.Which term of the AP 4, 8, 12, 16, … is 88? (a) 23rd (b) 21st (c) 24th (d) 22nd
  32. 32.What is the sum of the first 27 odd numbers (1 + 3 + 5 + …)? (a) 756 (b) 378 (c) 53 (d) 729
  33. 33.What is the sum of the first 5 terms of the AP 2, 5, 8, …? (a) 43 (b) 14 (c) 40 (d) 80
  34. 34.What is the 35th term of the AP 5, 7, 9, 11, …? (a) 73 (b) 68 (c) 70 (d) 75
  35. 35.What is the 21st term of the AP 16, 19, 22, 25, …? (a) 79 (b) 60 (c) 63 (d) 76
  36. 36.What is the 40th term of the AP 17, 25, 33, 41, …? (a) 312 (b) 337 (c) 320 (d) 329
  37. 37.Which term of the AP 13, 21, 29, 37, … is 229? (a) 30th (b) 28th (c) 27th (d) 29th
  38. 38.What is the sum of the first 7 terms of the AP 3, 5, 7, …? (a) 126 (b) 15 (c) 70 (d) 63
  39. 39.What is the sum of the first 10 terms of the AP 6, 10, 14, …? (a) 480 (b) 240 (c) 42 (d) 260
  40. 40.What is the sum of the first 7 terms of the AP 10, 14, 18, …? (a) 308 (b) 168 (c) 34 (d) 154

Answer key

  1. 22
  2. 240
  3. 55
  4. 60
  5. 21st
  6. 178
  7. 17
  8. 36
  9. 51
  10. 20th
  11. 300
  12. 2556
  13. 66
  14. 58
  15. 23
  16. 28th
  17. 45
  18. 194
  19. 154
  20. 150
  21. 290
  22. 325
  23. 32
  24. 175
  25. 51
  26. 256
  27. 49
  28. 38th
  29. 35
  30. 820
  31. 22nd
  32. 729
  33. 40
  34. 73
  35. 76
  36. 329
  37. 28th
  38. 63
  39. 240
  40. 154

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