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Arithmetic Progression Worksheet for Olympiad

Maths Olympiad topic 29: Sequences and AP · Set 635 · 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 9 terms of the AP 3, 4, 5, …? (a) 64 (b) 126 (c) 11 (d) 63
  2. 2.What is the 30th term of the AP 16, 19, 22, 25, …? (a) 90 (b) 87 (c) 103 (d) 106
  3. 3.What is the sum of the first 10 terms of the AP 1, 5, 9, …? (a) 380 (b) 37 (c) 210 (d) 190
  4. 4.What is the missing term in the AP 9, 13, 17, ?, 25? (a) 20 (b) 22 (c) 25 (d) 21
  5. 5.What is the sum of the first 11 terms of the AP 2, 7, 12, …? (a) 594 (b) 302 (c) 297 (d) 52
  6. 6.What is the missing term in the AP 18, 23, ?, 33, 38? (a) 27 (b) 28 (c) 33 (d) 29
  7. 7.What is the 26th term of the AP 13, 15, 17, 19, …? (a) 63 (b) 52 (c) 65 (d) 50
  8. 8.What is the sum of the first 23 odd numbers (1 + 3 + 5 + …)? (a) 552 (b) 276 (c) 45 (d) 529
  9. 9.What is the sum of all the whole numbers from 1 to 36? (a) 630 (b) 666 (c) 648 (d) 1332
  10. 10.What is the 31st term of the AP 13, 18, 23, 28, …? (a) 155 (b) 163 (c) 150 (d) 168
  11. 11.What is the 13th term of the AP 5, 14, 23, 32, …? (a) 117 (b) 122 (c) 113 (d) 108
  12. 12.What is the missing term in the AP 1, 8, ?, 22, 29? (a) 16 (b) 14 (c) 22 (d) 15
  13. 13.Which term of the AP 4, 6, 8, 10, … is 44? (a) 20th (b) 21st (c) 22nd (d) 23rd
  14. 14.What is the sum of the first 12 odd numbers (1 + 3 + 5 + …)? (a) 23 (b) 144 (c) 156 (d) 78
  15. 15.Which term of the AP 11, 19, 27, 35, … is 275? (a) 35th (b) 33rd (c) 34th (d) 36th
  16. 16.Which term of the AP 12, 21, 30, 39, … is 102? (a) 10th (b) 12th (c) 11th (d) 13th
  17. 17.What is the sum of the first 11 terms of the AP 2, 4, 6, …? (a) 132 (b) 143 (c) 264 (d) 22
  18. 18.What is the 16th term of the AP 11, 17, 23, 29, …? (a) 90 (b) 107 (c) 96 (d) 101
  19. 19.What is the sum of the first 5 terms of the AP 9, 13, 17, …? (a) 170 (b) 95 (c) 85 (d) 25
  20. 20.What is the sum of all the whole numbers from 1 to 93? (a) 4278 (b) 4372 (c) 4371 (d) 8742
  21. 21.What is the missing term in the AP 6, ?, 12, 15, 18? (a) 12 (b) 9 (c) 8 (d) 10
  22. 22.What is the 18th term of the AP 18, 25, 32, 39, …? (a) 137 (b) 119 (c) 144 (d) 126
  23. 23.What is the missing term in the AP 16, ?, 24, 28, 32? (a) 19 (b) 24 (c) 21 (d) 20
  24. 24.What is the 22nd term of the AP 11, 16, 21, 26, …? (a) 110 (b) 105 (c) 121 (d) 116
  25. 25.What is the sum of all the whole numbers from 1 to 13? (a) 78 (b) 182 (c) 91 (d) 92
  26. 26.What is the 22nd term of the AP 14, 20, 26, 32, …? (a) 146 (b) 140 (c) 132 (d) 126
  27. 27.What is the missing term in the AP 14, 22, ?, 38, 46? (a) 31 (b) 29 (c) 38 (d) 30
  28. 28.Which term of the AP 8, 11, 14, 17, … is 29? (a) 9th (b) 10th (c) 8th (d) 7th
  29. 29.What is the sum of the first 9 terms of the AP 10, 15, 20, …? (a) 275 (b) 540 (c) 50 (d) 270
  30. 30.What is the missing term in the AP 18, 25, ?, 39, 46? (a) 39 (b) 32 (c) 33 (d) 31
  31. 31.Which term of the AP 1, 4, 7, 10, … is 40? (a) 13th (b) 15th (c) 14th (d) 16th
  32. 32.What is the sum of the first 19 odd numbers (1 + 3 + 5 + …)? (a) 37 (b) 380 (c) 190 (d) 361
  33. 33.Which term of the AP 5, 7, 9, 11, … is 79? (a) 39th (b) 40th (c) 38th (d) 37th
  34. 34.What is the sum of the first 11 terms of the AP 10, 16, 22, …? (a) 70 (b) 473 (c) 880 (d) 440
  35. 35.What is the sum of the first 11 terms of the AP 3, 8, 13, …? (a) 308 (b) 616 (c) 313 (d) 53
  36. 36.What is the missing term in the AP 12, 15, 18, ?, 24? (a) 22 (b) 20 (c) 24 (d) 21
  37. 37.What is the 27th term of the AP 16, 18, 20, 22, …? (a) 54 (b) 52 (c) 68 (d) 70
  38. 38.Which term of the AP 18, 21, 24, 27, … is 87? (a) 25th (b) 23rd (c) 24th (d) 29th
  39. 39.What is the 25th term of the AP 9, 15, 21, 27, …? (a) 144 (b) 150 (c) 153 (d) 159
  40. 40.What is the sum of the first 12 terms of the AP 2, 7, 12, …? (a) 57 (b) 354 (c) 708 (d) 384

Answer key

  1. 63
  2. 103
  3. 190
  4. 21
  5. 297
  6. 28
  7. 63
  8. 529
  9. 666
  10. 163
  11. 113
  12. 15
  13. 21st
  14. 144
  15. 34th
  16. 11th
  17. 132
  18. 101
  19. 85
  20. 4371
  21. 9
  22. 137
  23. 20
  24. 116
  25. 91
  26. 140
  27. 30
  28. 8th
  29. 270
  30. 32
  31. 14th
  32. 361
  33. 38th
  34. 440
  35. 308
  36. 21
  37. 68
  38. 24th
  39. 153
  40. 354

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