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Arithmetic Progression Worksheet for Olympiad

Maths Olympiad topic 29: Sequences and AP · Set 816 · 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 24th term of the AP 7, 14, 21, 28, …? (a) 175 (b) 169 (c) 168 (d) 161
  2. 2.What is the sum of the first 30 odd numbers (1 + 3 + 5 + …)? (a) 59 (b) 900 (c) 930 (d) 465
  3. 3.What is the missing term in the AP 20, 28, ?, 44, 52? (a) 36 (b) 35 (c) 37 (d) 44
  4. 4.What is the sum of the first 11 terms of the AP 1, 2, 3, …? (a) 67 (b) 66 (c) 11 (d) 132
  5. 5.What is the sum of the first 5 terms of the AP 5, 7, 9, …? (a) 90 (b) 13 (c) 45 (d) 50
  6. 6.What is the sum of the first 5 odd numbers (1 + 3 + 5 + …)? (a) 9 (b) 30 (c) 25 (d) 15
  7. 7.What is the missing term in the AP 6, 10, 14, ?, 22? (a) 18 (b) 19 (c) 17 (d) 22
  8. 8.What is the 14th term of the AP 4, 13, 22, 31, …? (a) 126 (b) 121 (c) 130 (d) 117
  9. 9.What is the sum of all the whole numbers from 1 to 75? (a) 2851 (b) 2775 (c) 2850 (d) 5700
  10. 10.What is the sum of all the whole numbers from 1 to 97? (a) 9506 (b) 4754 (c) 4753 (d) 4656
  11. 11.What is the missing term in the AP 8, 16, 24, ?, 40? (a) 33 (b) 31 (c) 32 (d) 40
  12. 12.What is the sum of the first 27 odd numbers (1 + 3 + 5 + …)? (a) 378 (b) 53 (c) 756 (d) 729
  13. 13.What is the missing term in the AP 20, ?, 28, 32, 36? (a) 24 (b) 23 (c) 25 (d) 28
  14. 14.What is the 10th term of the AP 15, 20, 25, 30, …? (a) 50 (b) 65 (c) 60 (d) 45
  15. 15.What is the sum of the first 21 odd numbers (1 + 3 + 5 + …)? (a) 462 (b) 41 (c) 441 (d) 231
  16. 16.What is the 17th term of the AP 13, 18, 23, 28, …? (a) 93 (b) 80 (c) 98 (d) 85
  17. 17.What is the 38th term of the AP 4, 6, 8, 10, …? (a) 76 (b) 74 (c) 80 (d) 78
  18. 18.What is the missing term in the AP 2, ?, 6, 8, 10? (a) 5 (b) 3 (c) 6 (d) 4
  19. 19.What is the sum of the first 6 terms of the AP 2, 3, 4, …? (a) 30 (b) 54 (c) 7 (d) 27
  20. 20.What is the 11th term of the AP 10, 17, 24, 31, …? (a) 77 (b) 80 (c) 70 (d) 87
  21. 21.Which term of the AP 14, 19, 24, 29, … is 204? (a) 41st (b) 40th (c) 39th (d) 38th
  22. 22.What is the sum of the first 10 odd numbers (1 + 3 + 5 + …)? (a) 100 (b) 19 (c) 55 (d) 110
  23. 23.What is the 29th term of the AP 4, 9, 14, 19, …? (a) 144 (b) 149 (c) 140 (d) 145
  24. 24.What is the sum of the first 5 terms of the AP 9, 11, 13, …? (a) 65 (b) 70 (c) 17 (d) 130
  25. 25.What is the sum of all the whole numbers from 1 to 23? (a) 552 (b) 277 (c) 253 (d) 276
  26. 26.What is the 17th term of the AP 12, 14, 16, 18, …? (a) 44 (b) 46 (c) 32 (d) 34
  27. 27.Which term of the AP 18, 23, 28, 33, … is 178? (a) 33rd (b) 35th (c) 34th (d) 32nd
  28. 28.What is the 27th term of the AP 7, 15, 23, 31, …? (a) 215 (b) 208 (c) 223 (d) 216
  29. 29.What is the 10th term of the AP 3, 5, 7, 9, …? (a) 23 (b) 21 (c) 20 (d) 18
  30. 30.What is the 27th term of the AP 3, 10, 17, 24, …? (a) 182 (b) 192 (c) 185 (d) 189
  31. 31.What is the sum of all the whole numbers from 1 to 27? (a) 351 (b) 379 (c) 756 (d) 378
  32. 32.Which term of the AP 1, 4, 7, 10, … is 52? (a) 20th (b) 18th (c) 19th (d) 17th
  33. 33.What is the missing term in the AP 14, ?, 30, 38, 46? (a) 22 (b) 23 (c) 30 (d) 21
  34. 34.What is the 29th term of the AP 10, 13, 16, 19, …? (a) 87 (b) 94 (c) 97 (d) 84
  35. 35.What is the sum of the first 16 odd numbers (1 + 3 + 5 + …)? (a) 136 (b) 272 (c) 31 (d) 256
  36. 36.What is the sum of the first 5 terms of the AP 7, 13, 19, …? (a) 31 (b) 110 (c) 190 (d) 95
  37. 37.Which term of the AP 10, 18, 26, 34, … is 194? (a) 26th (b) 23rd (c) 25th (d) 24th
  38. 38.What is the sum of the first 6 terms of the AP 10, 11, 12, …? (a) 150 (b) 78 (c) 75 (d) 15
  39. 39.Which term of the AP 2, 5, 8, 11, … is 56? (a) 19th (b) 20th (c) 18th (d) 21st
  40. 40.What is the 13th term of the AP 15, 20, 25, 30, …? (a) 80 (b) 65 (c) 60 (d) 75

Answer key

  1. 168
  2. 900
  3. 36
  4. 66
  5. 45
  6. 25
  7. 18
  8. 121
  9. 2850
  10. 4753
  11. 32
  12. 729
  13. 24
  14. 60
  15. 441
  16. 93
  17. 78
  18. 4
  19. 27
  20. 80
  21. 39th
  22. 100
  23. 144
  24. 65
  25. 276
  26. 44
  27. 33rd
  28. 215
  29. 21
  30. 185
  31. 378
  32. 18th
  33. 22
  34. 94
  35. 256
  36. 95
  37. 24th
  38. 75
  39. 19th
  40. 75

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